Existence and boundary regularity for degenerate phase transitions

Paolo Baroni; Tuomo Kuusi; Casimir Lindfors; José Miguel Urbano

doi:10.1137/17M1121585

Existence and boundary regularity for degenerate phase transitions

Paolo Baroni, Tuomo Kuusi, Casimir Lindfors, José Miguel Urbano

Department of Mathematics and Systems Analysis

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Abstract

We study the Cauchy–Dirichlet problem associated to a phase transition modeled upon the degenerate two-phase Stefan problem. We prove that weak solutions are continuous up to the parabolic boundary and quantify the continuity by deriving a modulus. As a byproduct, these a priori regularity results are used to prove the existence of a so-called physical solution.

Original language	English
Pages (from-to)	456-490
Number of pages	35
Journal	SIAM Journal on Mathematical Analysis
Volume	50
Issue number	1
DOIs	https://doi.org/10.1137/17M1121585
Publication status	Published - 1 Jan 2018
MoE publication type	A1 Journal article-refereed

Keywords

Boundary modulus of continuity
Degenerate equations
Intrinsic scaling
Stefan problem

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KW - Intrinsic scaling

KW - Stefan problem

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Existence and boundary regularity for degenerate phase transitions

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