A fully nonlinear transmission problem degenerating on the interface

TL;DR

This paper proves that solutions to a nonlinear transmission problem that degenerates at the interface are Hölder differentiable up to the interface, providing sharp pointwise regularity with optimal variable exponents and uniform estimates.

Contribution

It establishes the Hölder differentiability and sharp regularity of solutions to a nonlinear degenerating transmission problem with universal and optimal estimates.

Findings

Solutions are Hölder differentiable up to the interface.

Achieved sharp pointwise $C^{1,eta(ullet)}$ regularity with optimal variable exponent.

Provided uniform estimates for the solutions.

Abstract

In this paper we prove that solutions to a transmission problem degenerating on the interface are H\"older differentiable up to the interface with universal estimates. Furthermore, we obtain a sharper pointwise $C^{1,\alpha(\cdot)}$ with optimal variable exponent and uniform estimates.