Boundary regularity for a parabolic obstacle type problem

Abstract

We study the regularity of the free boundary, near contact points with the fixed boundary, for a parabolic free boundary problemWe will show that under certain regularity assumptions on the boundary data f the free boundary is a C 1 manifold up to the fixed boundary. We also show that the C 1 modulus of continuity is uniform for a certain, and specified, subclass of solutions.

Boundary Regularity and Nontransversal Intersection for the Fully Nonlinear Obstacle Problem

“…If this is not the case, the free boundary may approach the fixed boundary at an angle [2]. Several variations of the classical tangential touch problem in recent years have appeared in [3,[5][6][7]20]. It is of interest to study the largest function space for which uniform results hold.…”