Continuous solutions for a degenerate free boundary problem

Abstract

Abstract We prove existence of continuous solutions for $$\partial _t [\gamma \left( \theta \right)] - div(\left| {\nabla \theta } \right|^{p - 2} \nabla \theta ) \ni 0, p > 2$$ , where ? is a maximal monotone graph, by showing equicontinuity of a sequence of approximate solutions. Relations of this type are models for certain free boundary problems like the Stefan problem with nonlinear diffusion.