Nonlocal minimal surfaces
Analysis of PDEs
2009-05-11 v1
Abstract
The de Giorgi theory for minimal surfaces consists in studying sets whose indicator function is a (local) minimum of the BV norm. In this paper we replace the BV norm by the norm, with , and try to understand what the minimisers look like. Parallel to the de Giorgi theory we prove that, if the boundary of a minimiser is sufficiently flat in the unit ball, then it is a smooth piece of hypersurface.
Cite
@article{arxiv.0905.1183,
title = {Nonlocal minimal surfaces},
author = {L. A. Caffarelli and J. -M. Roquejoffre and O. Savin},
journal= {arXiv preprint arXiv:0905.1183},
year = {2009}
}