Calculus of Variations and Geometric Measure Theory

A. Figalli - H. Shahgholian

A general class of free boundary problems for fully nonlinear elliptic equations

created by figalli on 19 Feb 2014


Accepted Paper

Inserted: 19 feb 2014
Last Updated: 19 feb 2014

Journal: Arch. Ration. Mech. Anal.
Year: 2014


In this paper we study a general class of fully nonlinear free boundary problems and we prove optimal regularity for solutions to this problem, namely, $W^{2,n}$ solutions are locally $C^{1,1}$. Under some extra conditions, we also show local regularity for the free boundary.