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arXiv · 1506.04281

Graph properties for nonlocal minimal surfaces

Serena Dipierro·Ovidiu Savin·Enrico Valdinoci
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Abstract

In this paper we show that a nonlocal minimal surface which is a graph outside a cylinder is in fact a graph in the whole of the space. As a consequence, in dimension~$3$, we show that the graph is smooth. The proofs rely on convolution techniques and appropriate integral estimates which show the pointwise validity of an Euler-Lagrange equation related to the nonlocal mean curvature.

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Serena Dipierro, Ovidiu Savin, Enrico Valdinoci. 2015-06-13. Graph properties for nonlocal minimal surfaces. https://arxiv.org/abs/1506.04281

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