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arXiv · 1706.05701

Flatness results for nonlocal minimal cones and subgraphs

Alberto Farina·Enrico Valdinoci
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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.

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Alberto Farina, Enrico Valdinoci. 2017-06-18. Flatness results for nonlocal minimal cones and subgraphs. https://arxiv.org/abs/1706.05701

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