Estudo Geralhttps://estudogeral.sib.uc.ptThe DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Wed, 03 Jun 2020 14:27:33 GMT2020-06-03T14:27:33Z5021A 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/10316/443982014-01-01T00:00:00ZLocal 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