Regularity of free boundaries of two‐phase problems for fully nonlinear elliptic equations of second order I. Lipschitz free boundaries are C1,

Abstract

In this paper, we study an extension of a C1,α regularity theory developed by L. Caffarelli in [2] to some fully nonlinear elliptic equations of second order. In fact, we investigate a two-phase free boundary problem in which a fully nonlinear elliptic equation of second order is verified by the solution in the positive and the negative domains. Assuming the free boundary is locally a Lipschitz graph, we have established the C1,α regularity of the free boundary. © 2000 John Wiley & Sons, Inc.