Nonlocal minimal surfaces

Details Nonlocal minimal surfaces Nonlocal minimal surfaces

2009-05-08

arxiv.org/abs/0905.1183v1

Mathematics

Analysis of PDEs

Scientific paper

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 $H^\sigma$ norm, with $\sigma<1/2$, 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.

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