A parabolic free boundary problem with Bernoulli type condition on the free boundary

In this talk we will investigate the regularity of the free boundary for a parabolic free boundary problem with constant gradient condition on the free boundary.

In particular, we will show that flat free boundary points are regular (in space). The proof is similar to, although somewhat simpler than, a proof used by Alt and Caffarelli to prove a similar result for elliptic problems.

This is a jount work with G.S. Weiss.