Calculus of Variations and Geometric Measure Theory

A. Figalli - H. Shahgholian

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

created by figalli on 19 Feb 2014


Accepted Paper

Inserted: 19 feb 2014
Last Updated: 19 feb 2014

Journal: Ann. Mat. Pura Appl.
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, $W^{2,n}_x\cap W^{1,n}_t$ solutions are locally $C^{1,1}_x \cap C^{0,1}_t$. A key tool for this result is a new BMO-type estimate which extends to the parabolic setting a previous result of Caffarelli-Huang. Under some extra conditions, we also show local regularity for the free boundary.