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arXiv · 1702.07159

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.

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Paolo Baroni, Tuomo Kuusi, Casimir Lindfors, José Miguel Urbano. 2017-02-23. Existence and boundary regularity for degenerate phase transitions. https://arxiv.org/abs/1702.07159

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