The structure of the free boundary in the fully nonlinear thin obstacle problem

TL;DR

This paper investigates the regularity of the free boundary in the fully nonlinear thin obstacle problem, proving that it is continuously differentiable near regular points, which advances understanding of free boundary smoothness.

Contribution

It establishes the $C^1$ regularity of the free boundary near regular points in the fully nonlinear thin obstacle problem, a novel result in this area.

Findings

Free boundary is $C^1$ near regular points

Advances understanding of free boundary regularity

Provides a foundation for further smoothness results

Abstract

We study the regularity of the free boundary in the fully nonlinear thin obstacle problem. Our main result establishes that the free boundary is $C^1$ near regular points.