Estudo GeralThe DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.https://estudogeral.sib.uc.pt2019-08-21T14:04:19Z2019-08-21T14:04:19Z5021Limits as p(x) of p(x)-harmonic functionsManfredi, Juan J.Rossi, Julio D.Urbano, José Miguelhttp://hdl.handle.net/10316/111752019-06-01T21:20:15Z2009-01-01T00:00:00ZTitle: 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.
2009-01-01T00:00:00Zp(x)-Harmonic functions with unbounded exponent in a subdomainManfredi, Juan J.Rossi, Julio D.Urbano, José Miguelhttp://hdl.handle.net/10316/112222019-06-01T21:20:19Z2008-01-01T00:00:00ZTitle: 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.
2008-01-01T00:00:00Z