# Regularity of free boundary in a parabolic problem without sign restriction

We consider a parabolic obstacle-type problem without sign restriction on the solution, for which we obtain the exact representation of the global solutions (i.e., solutions in the entire half-space $\{(x,t) \in \mathbb{R}^{n+1}: x_1>0\}$) and study the local properties of the free boundary near a fixed one. We also prove the smoothness of the free boundary under a homogeneous Dirichlet condition on the given boundary. This is a joint work with D. Apushkinskaya and N.N. Uraltseva.

This talk is part of the Applied and Computational Analysis Graduate Seminar series.