Graph properties for nonlocal minimal surfaces
Analysis of PDEs
2016-06-14 v5
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~, 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.
Cite
@article{arxiv.1506.04281,
title = {Graph properties for nonlocal minimal surfaces},
author = {Serena Dipierro and Ovidiu Savin and Enrico Valdinoci},
journal= {arXiv preprint arXiv:1506.04281},
year = {2016}
}