Existence and boundary regularity for degenerate phase transitions

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

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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 languageEnglish
Pages (from-to)456-490
Number of pages35
JournalSIAM Journal on Mathematical Analysis
Volume50
Issue number1
DOIs
Publication statusPublished - 1 Jan 2018
MoE publication typeA1 Journal article-refereed

Keywords

  • Boundary modulus of continuity
  • Degenerate equations
  • Intrinsic scaling
  • Stefan problem

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