Estudo Geralhttps://estudogeral.sib.uc.ptThe DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Fri, 19 Jul 2019 02:25:33 GMT2019-07-19T02:25:33Z50371- A proof of the C^p'-regularity conjecture in the plane p ′ -regularity conjecture in the planehttp://hdl.handle.net/10316/44401Title: A proof of the C^p'-regularity conjecture in the plane p ′ -regularity conjecture in the plane
Authors: Araújo, Damião J.; Teixeira, Eduardo V.; Urbano, José Miguel
Abstract: We establish a new oscillation estimate for solutions of nonlinear partial differential equations of elliptic, degenerate type. This new tool yields a precise control on the growth rate of solutions near their set of critical points, where ellipticity degenerates. As a consequence, we are able to prove the planar counterpart of the longstanding conjecture that solutions of the degenerate p-Poisson equation with a bounded source are locally of class C^p'=C^(1,1/(p-1)) ; this regularity is optimal.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10316/444012017-01-01T00:00:00Z
- Regularity for anisotropic fully nonlinear integro-differential equationshttp://hdl.handle.net/10316/44399Title: Regularity for anisotropic fully nonlinear integro-differential equations
Authors: Caffarelli, Luis A.; Leitão, Raimundo; Urbano, José Miguel
Abstract: We consider fully nonlinear integro-differential equations governed by kernels that have different homogeneities in different directions. We prove a nonlocal version of the ABP estimate, a Harnack inequality and the interior \(C^{1, \gamma }\) regularity, extending the results of Caffarelli and Silvestre (Comm Pure Appl Math 62:597–638, 2009) to the anisotropic case.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10316/443992014-01-01T00:00:00Z
- Towards the $C^{p^\prime}$-Regularity Conjecture in Higher Dimensionshttp://hdl.handle.net/10316/44406Title: Towards the $C^{p^\prime}$-Regularity Conjecture in Higher Dimensions
Authors: Araújo, Damião J.; Teixeira, Eduardo V.; Urbano, José Miguel
Abstract: A longstanding conjecture in elliptic regularity theory inquires whether a W^{1,p} function whose
p-laplacian is bounded is locally of class C^{1,\frac{1}{p-1}}. While it is well known that such functions are of class C^{1,\alpha} for some unknown 0 < α < 1, establishing the sharp estimate turns out to be a rather delicate problem. Quite recently, the authors managed to establish the conjecture in the plane. In this article, we address the conjecture in higher dimensions and confirm its validity in a number of other meaningful cases.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10316/444062017-01-01T00:00:00Z
- An intrinsic Liouville theorem for degenerate parabolic equationshttp://hdl.handle.net/10316/44397Title: An intrinsic Liouville theorem for degenerate parabolic equations
Authors: Teixeira, Eduardo V.; Urbano, José Miguel
Abstract: We show that weak solutions of the degenerate p−Laplace equation u_t - {\rm div}\left( |\nabla u|^{p-2}\nabla u \right) = 0,\quad p > 2 in the whole space are constant if their growth at infinity is properly controlled in an intrinsic manner.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10316/443972014-01-01T00:00:00Z
- On the Bulk Velocity of Brownian Ratchetshttp://hdl.handle.net/10316/44427Title: On the Bulk Velocity of Brownian Ratchets
Authors: Kondratyev, Stanislav; Urbano, José Miguel; Vorotnikov, Dmitry
Abstract: In this paper we study the unidirectional transport effect for Brownian ratchets modeled by Fokker--Planck-type equations. In particular, we consider the adiabatic and semiadiabatic limits for tilting ratchets, generic ratchets with small diffusion, and the multistate chemical ratchets. Having established a linear relation between the bulk transport velocity and the biperiodic solution, and using relative entropy estimates and new functional inequalities, we obtain explicit asymptotic formulas for the transport velocity and qualitative results concerning the direction of transport. In particular, we prove the conjecture by Blanchet, Dolbeault, and Kowalczyk that the bulk velocity of the stochastic Stokes' drift is nonzero for every nonconstant potential.
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10316/444272016-01-01T00:00:00Z
- Analysis of adaptive forward-backward diffusion flows with applications in image processinghttp://hdl.handle.net/10316/44400Title: Analysis of adaptive forward-backward diffusion flows with applications in image processing
Authors: Prasath, V B Surya; Urbano, José Miguel; Vorotnikov, Dmitry
Abstract: The nonlinear diffusion model introduced by Perona and Malik (1990 IEEE Trans. Pattern Anal. Mach. Intell. 12 629–39) is well suited to preserve salient edges while restoring noisy images. This model overcomes well-known edge smearing effects of the heat equation by using a gradient dependent diffusion function. Despite providing better denoizing results, the analysis of the PM scheme is difficult due to the forward-backward nature of the diffusion flow. We study a related adaptive forward-backward diffusion equation which uses a mollified inverse gradient term engrafted in the diffusion term of a general nonlinear parabolic equation. We prove a series of existence, uniqueness and regularity results for viscosity, weak and dissipative solutions for such forward-backward diffusion flows. In particular, we introduce a novel functional framework for wellposedness of flows of total variation type. A set of synthetic and real image processing examples are used to illustrate the properties and advantages of the proposed adaptive forward-backward diffusion flows.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10316/444002015-01-01T00:00:00Z
- A Quantitative Modulus of Continuity for the Two-Phase Stefan Problemhttp://hdl.handle.net/10316/44398Title: A Quantitative Modulus of Continuity for the Two-Phase Stefan Problem
Authors: Baroni, Paolo; Kuusi, Tuomo; Urbano, José Miguel
Abstract: We derive the quantitative modulus of continuity \omega(r)=\left[ p+\ln \left( \frac{r_0}{r}\right)\right]^{-\alpha (n, p)}, which we conjecture to be optimal for solutions of the p-degenerate two-phase Stefan problem. Even in the classical case p = 2, this represents a twofold improvement with respect to the early 1980’s state-of-the-art results by Caffarelli– Evans (Arch Rational Mech Anal 81(3):199–220, 1983) and DiBenedetto (Ann Mat Pura Appl 103(4):131–176, 1982), in the sense that we discard one logarithm iteration and obtain an explicit value for the exponent α(n, p).
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10316/443982014-01-01T00:00:00Z
- Analysis of adaptive forward-backward diffusion flows with applications in image processinghttp://hdl.handle.net/10316/43904Title: Analysis of adaptive forward-backward diffusion flows with applications in image processing
Authors: Prasath, V B Surya; Urbano, José Miguel; Vorotnikov, Dmitry
Abstract: The nonlinear diffusion model introduced by Perona and Malik (1990 IEEE Trans. Pattern Anal. Mach. Intell. 12 629–39) is well suited to preserve salient edges while restoring noisy images. This model overcomes well-known edge smearing effects of the heat equation by using a gradient dependent diffusion function. Despite providing better denoizing results, the analysis of the PM scheme is difficult due to the forward-backward nature of the diffusion flow. We study a related adaptive forward-backward diffusion equation which uses a mollified inverse gradient term engrafted in the diffusion term of a general nonlinear parabolic equation. We prove a series of existence, uniqueness and regularity results for viscosity, weak and dissipative solutions for such forward-backward diffusion flows. In particular, we introduce a novel functional framework for wellposedness of flows of total variation type. A set of synthetic and real image processing examples are used to illustrate the properties and advantages of the proposed adaptive forward-backward diffusion flows.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10316/439042015-01-01T00:00:00Z
- A free boundary optimization problem for the ∞-Laplacianhttp://hdl.handle.net/10316/43765Title: A free boundary optimization problem for the ∞-Laplacian
Authors: Teymurazyan, Rafayel; Urbano, José Miguel
Abstract: We study a free boundary optimization problem in heat conduction, ruled by the infinity–Laplace operator, with lower temperature bound and a volume constraint. We obtain existence and regularity results and derive geometric properties for the solution and the free boundaries.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10316/437652017-01-01T00:00:00Z
- Current issues on singular and degenerate evolution equationshttp://hdl.handle.net/10316/11429Title: Current issues on singular and degenerate evolution equations
Authors: Dibenedetto, Emmanuele; Urbano, José Miguel; Vespri, Vincenzo
Wed, 01 Jan 2003 00:00:00 GMThttp://hdl.handle.net/10316/114292003-01-01T00:00:00Z
- Unidirectional steady flow of a viscoelastic fluid with a free surfacehttp://hdl.handle.net/10316/11473Title: Unidirectional steady flow of a viscoelastic fluid with a free surface
Authors: Urbano, José Miguel; Videman, Juha H.
Abstract: We study the steady flow of a second grade fluid down an open inclined
channel. We formulate the mathematical problem, a mixed boundary value
problem for the Laplacian with an unknown free boundary described by a
nonlinear second order ODE, and prove existence of a unique solution for
small data using a contraction argument.
Sat, 01 Jan 2000 00:00:00 GMThttp://hdl.handle.net/10316/114732000-01-01T00:00:00Z
- A Free Boundary Problem: contributions from modern analysishttp://hdl.handle.net/10316/11476Title: A Free Boundary Problem: contributions from modern analysis
Authors: Urbano, José Miguel
Abstract: We exemplify the role of Free Boundary Problems as an important
source of ideas in modern analysis. With the help of a model problem we
illustrate the use of analytical, algebraic and geometrical techniques obtaining
uniqueness of weak solutions via the use of entropy inequalities, existence
through nonlinear semigroup theory, and regularity using a method, called
intrinsic scaling, based on interpreting a partial differential equation in a
geometry dictated by its own structure
Sat, 01 Jan 2000 00:00:00 GMThttp://hdl.handle.net/10316/114762000-01-01T00:00:00Z
- Hölder continuity of local weak solutions for parabolic equations exhibiting two degeneracieshttp://hdl.handle.net/10316/11553Title: Hölder continuity of local weak solutions for parabolic equations exhibiting two degeneracies
Authors: Urbano, José Miguel
Abstract: We consider equations of the form
atv - div(Q ( v)Vv) == 0 ,
where v E [0,1] and Q(v) degenerates for v == 0 and v == 1. We show that
local weak solutions are locally Holder continuous provided Q behaves like
a power near the two degeneracies. We adopt the technique of intrinsic
rescaling developed by DiBenedetto.
Fri, 01 Jan 1999 00:00:00 GMThttp://hdl.handle.net/10316/115531999-01-01T00:00:00Z
- On the stationary Boussinesq-Stefan problem with constitutive power-lawshttp://hdl.handle.net/10316/4667Title: On the stationary Boussinesq-Stefan problem with constitutive power-laws
Authors: Rodrigues, José Francisco; Urbano, José Miguel
Abstract: We discuss the existence of weak solutions to a steady-state coupled system between a two-phase Stefan problem, with convection and non-Fourier heat diffusion, and an elliptic variational inequality traducing the non-Newtonian flow only in the liquid phase. In the Stefan problem for the p-Laplacian equation the main restriction comes from the requirement that the liquid zone is at least an open subset, a fact that leads us to search for a continuous temperature field. Through the heat convection coupling term, this depends on the q-integrability of the velocity gradient and the imbedding theorems of Sobolev. We show that the appropriate condition for the continuity to hold, combining these two powers, is pq> n. This remarkably simple condition, together with q> 3n/(n + 2), that assures the compactness of the convection term, is sufficient to obtain weak solvability results for the interesting space dimension cases n = 2 and n = 3.
Thu, 01 Jan 1998 00:00:00 GMThttp://hdl.handle.net/10316/46671998-01-01T00:00:00Z
- New global a prior; estimates for the third-grade fluid equationshttp://hdl.handle.net/10316/8219Title: New global a prior; estimates for the third-grade fluid equations
Authors: Steinhauer, Mark; Urbano, José Miguel; Videman, Juha
Abstract: This note bridges the gap between the existence and regularity classes for the third-grade Rivlin-Ericksen fluid equations. We obtain a new global a priori estimate, which conveys the precise regularity conditions that lead to the existence of a global in time regular solution. Copyright © 2006 John Wiley & Sons, Ltd.
Sun, 01 Jan 2006 00:00:00 GMThttp://hdl.handle.net/10316/82192006-01-01T00:00:00Z
- Degenerate Elliptic Problems in a Class of Free Domainshttp://hdl.handle.net/10316/4659Title: Degenerate Elliptic Problems in a Class of Free Domains
Authors: Rodrigues, José Francisco; Urbano, José Miguel
Abstract: We study a mixed boundary value problem for an operator of p-Laplacian type. The main feature of the problem is the fact that the exact domain where it is considered is not known a priori and is to be determined so that a certain integral condition is satisfied. We establish the existence of a unique solution to the problem, by means of the analysis of the range of an appropriate real function, and we show the continuous dependence with respect to a family of operators. These results can be applied to the study of unidirectional non-Newtonian flows of power-law type, in particular to solve a simplified problem arising in theoretical glaciology and to show the existence of a Bingham flow in an open channel; the uniqueness in this case is an open problem.
Fri, 01 Jan 1999 00:00:00 GMThttp://hdl.handle.net/10316/46591999-01-01T00:00:00Z
- Entropy solutions for the p(x)-Laplace equationhttp://hdl.handle.net/10316/11376Title: Entropy solutions for the p(x)-Laplace equation
Authors: Sanchón, Manel; Urbano, José Miguel
Abstract: We consider a Dirichlet problem in divergence form with variable growth,
modeled on the p(x)-Laplace equation. We obtain existence and uniqueness of an entropy
solution for L1 data, extending the work of B´enilan et al. [5] to nonconstant exponents, as
well as integrability results for the solution and its gradient. The proofs rely crucially on a
priori estimates in Marcinkiewicz spaces with variable exponent
Sun, 01 Jan 2006 00:00:00 GMThttp://hdl.handle.net/10316/113762006-01-01T00:00:00Z
- On a two-sidedly degenerate chemotaxis model with volume-filling effecthttp://hdl.handle.net/10316/11371Title: On a two-sidedly degenerate chemotaxis model with volume-filling effect
Authors: Bendahmane, Mostafa; Karlsen, Kenneth H.; Urbano, José Miguel
Abstract: We consider a fully parabolic model for chemotaxis with volume-filling
effect and a nonlinear diffusion that degenerates in a two-sided fashion. We address
the questions of existence of weak solutions and of their regularity by using,
respectively, a regularization method and the technique of intrinsic scaling.
Sun, 01 Jan 2006 00:00:00 GMThttp://hdl.handle.net/10316/113712006-01-01T00:00:00Z
- New global a priori estimates for the third-grade fluid equationshttp://hdl.handle.net/10316/11394Title: New global a priori estimates for the third-grade fluid equations
Authors: Steinhauer, Mark; Urbano, José Miguel; Videman, Juha
Abstract: This note bridges the gap between the existence and regularity classes
for the solutions of the third-grade Rivlin-Ericksen fluid equations. We obtain a
new global a priori estimate which conveys the precise regularity conditions that
lead to the existence of a global in time regular solution
Sat, 01 Jan 2005 00:00:00 GMThttp://hdl.handle.net/10316/113942005-01-01T00:00:00Z
- Boundary regularity at {t=0} for a singular free boundary problemhttp://hdl.handle.net/10316/11383Title: Boundary regularity at {t=0} for a singular free boundary problem
Authors: Henriques, Eurica; Urbano, José Miguel
Abstract: In this note it is shown that the weak solutions of the Stefan problem
for the singular p-Laplacian are continuous up to {t = 0}. The result is a follow-up
to a recent paper of the authors concerning the interior regularity
Sat, 01 Jan 2005 00:00:00 GMThttp://hdl.handle.net/10316/113832005-01-01T00:00:00Z
- On the doubly singular equation g(u)t= Dpuhttp://hdl.handle.net/10316/11421Title: On the doubly singular equation g(u)t= Dpu
Authors: Henriques, Eurica; Urbano, José Miguel
Abstract: We prove that local weak solutions of a nonlinear parabolic equation
with a doubly singular character are locally continuous. One singularity occurs in
the time derivative and is due to the presence of a maximal monotone graph; the
other comes up in the principal part of the PDE, where the p-Laplace operator is
considered. The paper extends to the singular case 1 < p < 2, the results obtained
previously by the second author for the degenerate case p > 2; it completes a
regularity theory for a type of PDEs that model phase transitions for a material
obeying a nonlinear law of di usion.
Thu, 01 Jan 2004 00:00:00 GMThttp://hdl.handle.net/10316/114212004-01-01T00:00:00Z
- Intrinsic scaling for pde's with an exponential nonlinearityhttp://hdl.handle.net/10316/11403Title: Intrinsic scaling for pde's with an exponential nonlinearity
Authors: Henriques, Eurica; Urbano, José Miguel
Abstract: We consider strongly degenerate equations in divergence form of the
type ∂tu − ∇ • (|u|γ(x,t)∇u)= f , where the exponential nonlinearity satisfies the condition 0 < γ− ≤ γ(x, t) ≤ γ+. We show, by means of intrinsic scaling, that weak solutions are locally continuous.
Thu, 01 Jan 2004 00:00:00 GMThttp://hdl.handle.net/10316/114032004-01-01T00:00:00Z
- Growth conditions and uniqueness of the Cauchy problem for the evolutionary infinity Laplacianhttp://hdl.handle.net/10316/11223Title: Growth conditions and uniqueness of the Cauchy problem for the evolutionary infinity Laplacian
Authors: Leonori, Tommaso; Urbano, José Miguel
Abstract: We study the Cauchy problem for the parabolic infinity Laplace equation.
We prove a new comparison principle and obtain uniqueness of viscosity
solutions in the class of functions with a polinomial growth at infinity, improving
previous results obtained assuming a linear growth.
Tue, 01 Jan 2008 00:00:00 GMThttp://hdl.handle.net/10316/112232008-01-01T00:00:00Z
- Quasi-steady Stokes flow of multiphase fluids with shear-dependent viscosityhttp://hdl.handle.net/10316/11346Title: Quasi-steady Stokes flow of multiphase fluids with shear-dependent viscosity
Authors: Ebmeyer, Carsten; Urbano, José Miguel
Abstract: The quasi–steady power–law Stokes flow of a mixture of incompressible fluids
with shear–dependent viscosity is studied. The fluids are immiscible and have constant
densities. Existence results are presented for both the no–slip and the no–stick boundary
value conditions. Use is made of Schauder’s fixed–point theorem, compactness arguments,
and DiPerna-Lions renormalized solutions.
Sun, 01 Jan 2006 00:00:00 GMThttp://hdl.handle.net/10316/113462006-01-01T00:00:00Z
- On the well-posedness of a two-phase minimization problemhttp://hdl.handle.net/10316/13715Title: On the well-posedness of a two-phase minimization problem
Authors: Urbano, José Miguel; Vorotnikov, Dmitry
Abstract: We prove a series of results concerning the emptiness and non-emptiness
of a certain set of Sobolev functions related to the well-posedness of a two-phase
minimization problem, involving both the p(x)-norm and the in nity norm. The
results, although interesting in their own right, hold the promise of a wider applicability
since they can be relevant in the context of other problems where minimization
of the p-energy in a part of the domain is coupled with the more local minimization
of the L1-norm on another region
Fri, 01 Jan 2010 00:00:00 GMThttp://hdl.handle.net/10316/137152010-01-01T00:00:00Z
- On a Darcy-Stefan Problem arising in freezing and thawing of saturated porous mediahttp://hdl.handle.net/10316/11231Title: On a Darcy-Stefan Problem arising in freezing and thawing of saturated porous media
Authors: Rodrigues, José Francisco; Urbano, José Miguel
Abstract: A model with phase change for material convection in a saturated
porous medium with a frozen region is formulated as a Darcy-Stefan problem. We propose a new generalized formulation for this Stefan-type problem with convection governed by Darcy’s law. This approach, which is
valid for irregular geometries with irregular subregions, has the advantage
of not requiring the smoothness of the temperature, that restricted previous mathematical works to two-dimensional particular cases. We show
existence of generalized solutions, passing to the limit in suitable approximated problems, which in principle can be solved numerically by the finite
element method.
Thu, 01 Jan 1998 00:00:00 GMThttp://hdl.handle.net/10316/112311998-01-01T00:00:00Z
- p(x)-Harmonic functions with unbounded exponent in a subdomainhttp://hdl.handle.net/10316/11222Title: p(x)-Harmonic functions with unbounded exponent in a subdomain
Authors: Manfredi, Juan J.; Rossi, Julio D.; Urbano, José Miguel
Abstract: We study the Dirichlet problem −div(|∇u|p(x)−2∇u) = 0 in
, with
u = f on @
and p(x) = ∞ in D, a subdomain of the reference domain
. The main
issue is to give a proper sense to what a solution is. To this end, we consider the limit
as n → ∞ of the solutions un to the corresponding problem when pn(x) = p(x)∧ n,
in particular, with p = n in D. Under suitable assumptions on the data, we find
that such a limit exists and that it can be characterized as the unique solution of a
variational minimization problem. Moreover, we examine this limit in the viscosity
sense and find an equation it satisfies.
Tue, 01 Jan 2008 00:00:00 GMThttp://hdl.handle.net/10316/112222008-01-01T00:00:00Z
- On a doubly nonlinear diffusion model of chemotaxis with prevention of overcrowdinghttp://hdl.handle.net/10316/11234Title: On a doubly nonlinear diffusion model of chemotaxis with prevention of overcrowding
Authors: Bendahmane, Mostafa; Bürger, Raimund; Baier, Ricardo Ruiz; Urbano, José Miguel
Abstract: This paper addresses the existence and regularity of weak solutions for
a fully parabolic model of chemotaxis, with prevention of overcrowding, that degenerates
in a two-sided fashion, including an extra nonlinearity represented by a p-
Laplacian diffusion term. To prove the existence of weak solutions, a Schauder fixedpoint
argument is applied to a regularized problem and the compactness method is
used to pass to the limit. The local H¨older regularity of weak solutions is established
using the method of intrinsic scaling. The results are a contribution to showing,
qualitatively, to what extent the properties of the classical Keller-Segel chemotaxis
models are preserved in a more general setting. Some numerical examples illustrate
the model.
Tue, 01 Jan 2008 00:00:00 GMThttp://hdl.handle.net/10316/112342008-01-01T00:00:00Z
- The obstacle problem for nonlinear elliptic equations with variable growth and L1-datahttp://hdl.handle.net/10316/11321Title: The obstacle problem for nonlinear elliptic equations with variable growth and L1-data
Authors: Rodrigues, José Francisco; Sanchón, Manel; Urbano, José Miguel
Abstract: The aim of this paper is twofold: to prove, for L1-data, the existence and
uniqueness of an entropy solution to the obstacle problem for nonlinear elliptic equations
with variable growth, and to show some convergence and stability properties of the corresponding
coincidence set. The latter follow from extending the Lewy–Stampacchia inequalities
to the general framework of L1
Sun, 01 Jan 2006 00:00:00 GMThttp://hdl.handle.net/10316/113212006-01-01T00:00:00Z
- A mathematical model for a comprehensive approach to the dynamics of human colonic aberrant crypt focihttp://hdl.handle.net/10316/11197Title: A mathematical model for a comprehensive approach to the dynamics of human colonic aberrant crypt foci
Authors: Figueiredo, Isabel N.; Figueiredo, Pedro N.; Leal, Carlos; Urbano, José Miguel
Abstract: In this paper, we propose mathematical models for the growth dynamics
of aberrant crypt foci in the human colon, as well as for some of their
characteristics, namely the apoptosis and proliferation indices. The models rely on
logistic type differential equations and clinical observations at different times, and
can arguably be used as an auxiliary screening tool for colon cancer. We report
several results using available medical data.
Tue, 01 Jan 2008 00:00:00 GMThttp://hdl.handle.net/10316/111972008-01-01T00:00:00Z
- Limits as p(x) of p(x)-harmonic functionshttp://hdl.handle.net/10316/11175Title: Limits as p(x) of p(x)-harmonic functions
Authors: Manfredi, Juan J.; Rossi, Julio D.; Urbano, José Miguel
Abstract: In this note we study the limit as p(x) ! 1of solutions to − p(x)u = 0
in a domain
, with Dirichlet boundary conditions. Our approach consists in considering
sequences of variable exponents converging uniformly to +1 and analyzing
how the corresponding solutions of the problem converge and what equation is satisfied
by the limit.
Thu, 01 Jan 2009 00:00:00 GMThttp://hdl.handle.net/10316/111752009-01-01T00:00:00Z
- The nonlinear N-membranes evolution problemhttp://hdl.handle.net/10316/11203Title: The nonlinear N-membranes evolution problem
Authors: Rodrigues, José Francisco; Santos, Lisa; Urbano, José Miguel
Abstract: The parabolic N-membranes problem for the p-Laplacian and the complete
order constraint on the components of the solution is studied in what concerns
the approximation, the regularity and the stability of the variational solutions. We
extend to the evolutionary case the characterization of the Lagrange multipliers associated
with the ordering constraint in terms of the characteristic functions of the
coincidence sets. We give continuous dependence results, and study the asymptotic
behavior as t → ∞ of the solution and the coincidence sets, showing that they
converge to their stationary counterparts.
Tue, 01 Jan 2008 00:00:00 GMThttp://hdl.handle.net/10316/112032008-01-01T00:00:00Z
- Local Hölder continuity for doubly nonlinear parabolic equationshttp://hdl.handle.net/10316/13697Title: Local Hölder continuity for doubly nonlinear parabolic equations
Authors: Kuusi, Tuomo; Siljander, Juhana; Urbano, José Miguel
Abstract: We give a proof of the Hölder continuity of weak solutions of certain degenerate
doubly nonlinear parabolic equations in measure spaces. We only assume
the measure to be a doubling non-trivial Borel measure which supports a Poincaré
inequality. The proof discriminates between large scales, for which a Harnack inequality
is used, and small scales, that require intrinsic scaling methods.
Fri, 01 Jan 2010 00:00:00 GMThttp://hdl.handle.net/10316/136972010-01-01T00:00:00Z
- On the interior regularity of weak solutions to the 2-D incompressible Euler equationshttp://hdl.handle.net/10316/44405Title: On the interior regularity of weak solutions to the 2-D incompressible Euler equations
Authors: Siljander, Juhana; Urbano, José Miguel
Abstract: We study whether some of the non-physical properties observed for weak solutions of the incompressible Euler equations can be ruled out by studying the vorticity formulation. Our main contribution is in developing an interior regularity method in the spirit of De Giorgi–Nash–Moser, showing that local weak solutions are exponentially integrable, uniformly in time, under minimal integrability conditions. This is a Serrin-type interior regularity result \begin{aligned} u \in L_\mathrm{loc}^{2+\varepsilon }(\Omega _T) \implies \mathrm{local\ regularity} \end{aligned} for weak solutions in the energy space L_t^\infty L_x^2, satisfying appropriate vorticity estimates. We also obtain improved integrability for the vorticity—which is to be compared with the DiPerna–Lions assumptions. The argument is completely local in nature as the result follows from the structural properties of the equation alone, while completely avoiding all sorts of boundary conditions and related gradient estimates. To the best of our knowledge, the approach we follow is new in the context of Euler equations and provides an alternative look at interior regularity issues. We also show how our method can be used to give a modified proof of the classical Serrin condition for the regularity of the Navier–Stokes equations in any dimension.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10316/444052017-01-01T00:00:00Z
- Investigação científica em Portugal : uma obrigação moral para com as gerações vindourashttp://hdl.handle.net/10316/42384Title: Investigação científica em Portugal : uma obrigação moral para com as gerações vindouras
Authors: Urbano, José Miguel; Martins, Pedro; Fiolhais, Carlos
Tue, 01 Jan 1985 00:00:00 GMThttp://hdl.handle.net/10316/423841985-01-01T00:00:00Z
- Regularity in Sobolev spaces for doubly nonlinear parabolic equationshttp://hdl.handle.net/10316/11467Title: Regularity in Sobolev spaces for doubly nonlinear parabolic equations
Authors: Ebmeyer, Carsten; Urbano, José Miguel
Sat, 01 Jan 2000 00:00:00 GMThttp://hdl.handle.net/10316/114672000-01-01T00:00:00Z
- A singular-degenerate parabolic problem: regularity up to the Dirichlet boundaryhttp://hdl.handle.net/10316/11478Title: A singular-degenerate parabolic problem: regularity up to the Dirichlet boundary
Authors: Urbano, José Miguel
Abstract: We show that weak solutions of a free boundary problem, modeling a waterice
phase transition in the case of nonlinear heat diffusion, are continuous up to
the lateral boundary. We consider homogeneous Dirichlet boundary conditions and
assume that the lateral boundary of the space-time domain satisfies the property of
positive geometric density. The results are a follow up from recent results by the
author concerning the interior regularity.
Sat, 01 Jan 2000 00:00:00 GMThttp://hdl.handle.net/10316/114782000-01-01T00:00:00Z