Calculus of Variations and Geometric Measure Theory

A. Figalli - E. Valdinoci

Regularity and Bernstein-type results for nonlocal minimal surfaces

created by figalli on 27 Dec 2014


Accepted Paper

Inserted: 27 dec 2014
Last Updated: 27 dec 2014

Journal: J. Reine Angew. Math.
Year: 2014


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 $\R^n$.