WIAS Preprint No. 1831, (2013)

Regularity and Bernstein-type results for nonlocal minimal surfaces



Authors

  • Figalli, Alessio
  • Valdinoci, Enrico
    ORCID: 0000-0001-6222-2272

2010 Mathematics Subject Classification

  • 49Q05 35B65 35R11 28A75

Keywords

  • s-minimal surfaces, regularity theory, Bernstein's Theorem

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 as a consequence of the nonexistence of singular minimal cones in one dimension less.

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