Calculus of Variations and Geometric Measure Theory
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P. Baroni - T. Kuusi - C. Lindfors - J. M. Urbano

Existence and boundary regularity for degenerate phase transitions

created by baroni on 16 Feb 2017
modified on 31 Aug 2017


SIAM J. Math. Anal.

Inserted: 16 feb 2017
Last Updated: 31 aug 2017

Year: 2017

ArXiv: 1702.07159 PDF


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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