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
DOI
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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