Regularity and Bernstein-type results for nonlocal minimal surfaces

Alessio Figalli; Enrico Valdinoci

Regularity and Bernstein-type results for nonlocal minimal surfaces

Analysis of PDEs 2013-07-02 v1

Authors: Alessio Figalli , Enrico Valdinoci

Abstract

We prove that, in every dimension, Lipschitz nonlocal minimal surfaces are smooth. Also, we extend to the nonlocal setting a famous theorem of De Giorgi stating that the validity of Bernstein's theorem in dimension $n+1$ is a consequence of the nonexistence of $n$ -dimensional singular minimal cones in $\R^n$ .

Keywords

minimal surfaces lipschitz spaces del pezzo surfaces

Cite

@article{arxiv.1307.0234,
  title  = {Regularity and Bernstein-type results for nonlocal minimal surfaces},
  author = {Alessio Figalli and Enrico Valdinoci},
  journal= {arXiv preprint arXiv:1307.0234},
  year   = {2013}
}