Regularity of the singular set in the fully nonlinear obstacle problem (Q2693150)

Summary: For the obstacle problem involving a convex fully nonlinear elliptic operator, we show that the singular set in the free boundary stratifies. The top stratum is locally covered by a \(C^{1 , \alpha}\) manifold, and the lower strata are covered by \(C^{1 , \log^\varepsilon}\) manifolds. This recovers some of the recent regularity results due to Colombo-Spolaor-Velichkov (2018) and Figalli-Serra (2019) when the operator is the Laplacian.