The thin obstacle problem for some variable coefficient degenerate elliptic operators

TL;DR

This paper proves optimal regularity and smoothness of the free boundary in the thin obstacle problem for certain degenerate elliptic operators with variable coefficients.

Contribution

It establishes the regularity and smoothness results for a class of degenerate elliptic equations with variable coefficients, advancing understanding of the thin obstacle problem.

Findings

Optimal interior regularity of solutions.

$C^{1,gamma}$ smoothness of the free boundary.

Results applicable to a class of degenerate elliptic operators.

Abstract

In this paper we establish the optimal interior regularity and the $C^{1,\gamma}$ smoothness of the regular part of the free boundary in the thin obstacle problem for a class of degenerate elliptic equations with variable coefficients.