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

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

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 (US)
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
State	Published - Jan 1 2018
Externally published	Yes

ASJC Scopus subject areas

Computational Mathematics
Analysis
Applied Mathematics

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10.1137/17M1121585

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title = "Existence and boundary regularity for degenerate phase transitions",

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.",

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AU - Baroni, Paolo

AU - Kuusi, Tuomo

AU - Lindfors, Casimir

AU - Urbano, José Miguel

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N2 - 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.

AB - 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.

UR - https://epubs.siam.org/doi/10.1137/17M1121585

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U2 - 10.1137/17M1121585

DO - 10.1137/17M1121585

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JO - SIAM Journal on Mathematical Analysis

JF - SIAM Journal on Mathematical Analysis

IS - 1

ER -

Existence and boundary regularity for degenerate phase transitions

Abstract

ASJC Scopus subject areas

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