Free boundary regularity for fully nonlinear non-homogeneous two-phase problems

TL;DR

This paper proves that free boundaries in fully nonlinear two-phase problems with non-zero right hand side are smooth (C^{1,γ}) if they are initially flat or Lipschitz, advancing understanding of boundary regularity.

Contribution

It establishes C^{1,γ} regularity of free boundaries for fully nonlinear two-phase problems with non-zero right hand side, under flat or Lipschitz conditions.

Findings

Free boundaries are C^{1,γ} smooth.

Regularity holds for fully nonlinear elliptic operators.

Results apply to problems with non-zero right hand side.

Abstract

We prove that flat or Lipschitz free boundaries of two-phase free boundary problems governed by fully nonlinear uniformly elliptic operators and with non-zero right hand side are $C^{1,\gamma}$.