Existence and boundary regularity for degenerate phase transitions

2017/02/23 by Baroni, Paolo, Kuusi, Tuomo, Lindfors, Casimir +1
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1702.07159

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.

Related

• Improved moduli of continuity for degenerate phase transitions
• Logarithmic continuity for the Nonlocal degenerate two-phase Stefan problem
• Local continuity of weak solutions to the Stefan problem involving the singular p-Laplacian
• Regularity for solutions of the two-phase Stefan problem
• The Two-Phase Stefan Problem with Anomalous Diffusion