A singular-degenerate parabolic problem: regularity up to the Dirichlet boundary

Abstract

We show that weak solutions of a free boundary problem, modeling a waterice phase transition in the case of nonlinear heat diffusion, are continuous up to the lateral boundary. We consider homogeneous Dirichlet boundary conditions and assume that the lateral boundary of the space-time domain satisfies the property of positive geometric density. The results are a follow up from recent results by the author concerning the interior regularity.