Removable singularities for nonlocal minimal graphs

Abstract

We prove the removable singularity theorem for nonlocal minimal graphs. Specifically, we show that any nonlocal minimal graph in $\Omega \setminus K$, where $\Omega \subset {\mathbb{R}}^n$ is an open set and $K\subset \Omega$ is a compact set of $(s,1)$-capacity zero, is indeed a nonlocal minimal graph in all of $\Omega$.

16 pages

References in corpus (3)

• Gamma-convergence of nonlocal perimeter functionals
• Complete stickiness of nonlocal minimal surfaces for small values of the fractional parameter
• A gradient estimate for nonlocal minimal graphs