Flatness results for nonlocal minimal cones and subgraphs
Analysis of PDEs
2017-06-20 v1
Abstract
We show that nonlocal minimal cones which are non-singular subgraphs outside the origin are necessarily halfspaces. The proof is based on classical ideas of~\cite{DG1} and on the computation of the linearized nonlocal mean curvature operator, which is proved to satisfy a suitable maximum principle. With this, we obtain new, and somehow simpler, proofs of the Bernstein-type results for nonlocal minimal surfaces which have been recently established in~\cite{FV}. In addition, we establish a new nonlocal Bernstein-Moser-type result which classifies Lipschitz nonlocal minimal subgraphs outside a ball.
Keywords
Cite
@article{arxiv.1706.05701,
title = {Flatness results for nonlocal minimal cones and subgraphs},
author = {Alberto Farina and Enrico Valdinoci},
journal= {arXiv preprint arXiv:1706.05701},
year = {2017}
}