The singular set in the fully nonlinear obstacle problem

Analysis Seminar
Topic:The singular set in the fully nonlinear obstacle problem
Speaker:Ovidiu Savin
Affiliation:Columbia University
Date:Monday, November 18
Time/Room:5:00pm - 6:00pm/Simonyi Hall 101
Video Link:https://video.ias.edu/analysis/2019/1118-OvidiuSavin

For the Obstacle Problem involving a convex fully nonlinear elliptic operator, we show that the singular set of the free boundary stratifies. The top stratum is locally covered by a $C^{1,\alpha}$-manifold, and the lower strata are covered by $C^{1,\log^\eps}$-manifolds. This essentially recovers the regularity result obtained by Figalli-Serra when the operator is the Laplacian.