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arXiv · 0905.1183

Nonlocal minimal surfaces

L. A. Caffarelli·J. -M. Roquejoffre·O. Savin
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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 $H^σ$ norm, with $σ<1/2$, 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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L. A. Caffarelli, J. -M. Roquejoffre, O. Savin. 2009-05-08. Nonlocal minimal surfaces. https://arxiv.org/abs/0905.1183

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