Regularity of the trace of nonlocal minimal graphs

TL;DR

This paper proves that the boundary trace of nonlocal minimal graphs at sticky points is smoothly differentiable, establishing that boundary continuity leads to boundary differentiability in this context.

Contribution

It demonstrates the regularity of the trace at sticky points and links boundary continuity to differentiability for nonlocal minimal graphs.

Findings

Trace of nonlocal minimal graphs at stickiness points is $C^{1,gamma}$

Boundary continuity implies boundary differentiability for these graphs

Provides new regularity results for nonlocal minimal surfaces

Abstract

We prove that the trace of nonlocal minimal graphs at points of stickiness is of class~$C^{1,\gamma}$. As a result, we show that boundary continuity implies boundary differentiability for nonlocal minimal graphs.