Existence and Boundary Regularity for Degenerate Phase Transitions
Paolo Baroni, Tuomo Kuusi, Casimir Lindfors, José Miguel Urbano · SIAM Journal on Mathematical Analysis · 2018
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.