Regularity and Bernstein-type results for nonlocal minimal surfaces

2013/06/30 by Alessio Figalli, Enrico Valdinoci, Figalli, Alessio +1 · 1 citation
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP

paper · pdf · doi:10.48550/arxiv.1307.0234

arxiv created 2013/06/30 · arxiv updated 2013/07/02

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 in dimension n+1 is a consequence of the nonexistence of n-dimensional singular minimal cones in \Rⁿ.

Cited by

• Riesz fractional gradient functionals defined on partitions: nonlocal-to-local variational limits

Related

• Regularity properties of nonlocal minimal surfaces via limiting arguments
• Flatness results for nonlocal minimal cones and subgraphs
• Nonlocal minimal surfaces
• Regularity of nonlocal minimal cones in dimension 2
• Yau's conjecture for nonlocal minimal surfaces