Regularity of nonlocal minimal cones in dimension 2

Abstract

We show that the only nonlocal $s$-minimal cones in ${\mathbb{R}}^2$ are the trivial ones for all $s\in (0,1)$. As a consequence we obtain that the singular set of a nonlocal minimal surface has at most $n-3$ Hausdorff dimension.

Cited by in corpus (1)

• Nonlocal diffusion and applications