Seminari del Dipartimento di Matematica

Seminario del 2019

Ovidiu Savin, Columbia University, New York

The singular set in the fully nonlinear obstacle problem

nell'ambito della serie: SEMINARI DI ANALISI MATEMATICA BRUNO PINI

analisi matematica

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.