Boundary regularity for a fully nonlinear free transmission problem

Abstract

We examine boundary regularity for a fully nonlinear free transmission problem. We argue using approximation methods, comparing the operators driving the problem with a limiting profile. Working natural conditions on the data of the problem, we produce regularity estimates in Sobolev and $C^{1,\mathrm{Log}-\mathrm{Lip}}$-spaces. Our findings extend recent developments in the literature to the free boundary setting.