Regularity and Bernstein-type results for nonlocal minimal surfaces

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 [5] 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 IR. 

Topics

Cite this paper

@inproceedings{Figalli2013RegularityAB, title={Regularity and Bernstein-type results for nonlocal minimal surfaces}, author={Alessio Figalli and Enrico Valdinoci}, year={2013} }