Two-phase transition problems for fully nonlinear parabolic equations of second order

Abstract

In this paper we study an extension of a regularity theory presented by I. Athanasopoulos, L. Caffarelli and S. Salsa in [3], [4], to some fully nonlinear parabolic equations of second order. We investigate a two-phase free boundary problem in which a fully nonlinear parabolic equation is verified by the solution in the positive and the negative domain. We prove that the solution is Lipschitz up to the Lipschitz free boundary and that Lipschitz free boundaries are C 1 .