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arXiv · 1307.0234

Regularity and Bernstein-type results for nonlocal minimal surfaces

Alessio Figalli·Enrico Valdinoci
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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 $\R^n$.

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Alessio Figalli, Enrico Valdinoci. 2013-06-30. Regularity and Bernstein-type results for nonlocal minimal surfaces. https://arxiv.org/abs/1307.0234

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