A degenerate fully nonlinear free transmission problem with variable exponents

TL;DR

This paper investigates a class of complex free transmission problems with variable degeneracy, establishing optimal regularity results by connecting them to well-understood elliptic equations.

Contribution

It introduces a novel approach to analyze degenerate fully nonlinear free transmission problems with variable degeneracy rates, deriving optimal regularity estimates.

Findings

Established optimal pointwise regularity depending on degeneracy rate

Connected the problem to homogeneous fully nonlinear uniformly elliptic equations

Developed perturbation methods for analysis

Abstract

We study degenerate fully nonlinear free transmission problems, where the degeneracy rate varies in the domain. We prove optimal pointwise regularity depending on the degeneracy rate. Our arguments consist of perturbation methods, relating our problem to a homogeneous, fully nonlinear, uniformly elliptic equation.