Obstacle problem with a degenerate force term

We obtain a uniform $C^{1, 1}$ bound on cubic blowups; we find all homogeneous global solutions; we prove the uniqueness of the blowup limit; we prove the convergence of the free boundary to the free boundary of the blowup limit; at the points with lowest Weiss balanced energy, we prove the convergence of the normal of the free boundary to the normal of the free boundary of the blowup limit and that locally the free boundary is a graph; and, finally, for a particular case we prove that the free boundary is not $C^{1, α}$ regular near to a degenerate point for any $0 < α < 1$ .

Keywords

free boundary, obstacle problem, degenerate, blowup, regularity

Mathematical Subject Classification 2010

Primary: 35R35

Secondary: 35J60

Milestones

Received: 25 October 2014

Revised: 27 October 2015

Accepted: 6 January 2016

Published: 24 March 2016

Authors

Karen Yeressian
Institute of Mathematics University of Zurich Winterthurerstrasse 190 CH-8057 Zurich Switzerland

Vol. 9, No. 2, 2016

Karen Yeressian

Abstract

Keywords

Mathematical Subject Classification 2010

Milestones

Authors