Regularity and Bernstein-type results for nonlocal minimal surfaces
- Figalli, Alessio
- Valdinoci, Enrico
2010 Mathematics Subject Classification
- 49Q05 35B65 35R11 28A75
- s-minimal surfaces, regularity theory, Bernstein's Theorem
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.