Regularity and Bernstein-type results for nonlocal minimal surfaces

Alessio Figalli; Enrico Valdinoci

doi:10.1515/crelle-2015-0006

Regularity and Bernstein-type results for nonlocal minimal surfaces

Alessio Figalli, Enrico Valdinoci

Research output: Contribution to journal › Article › peer-review

41 Citations (Web of Science)

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 [6] 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.

Original language	English
Pages (from-to)	263-273
Number of pages	11
Journal	Journal fur die Reine und Angewandte Mathematik
Volume	2017
Issue number	729
Early online date	1 Jan 2015
DOIs	https://doi.org/10.1515/crelle-2015-0006
Publication status	Published - Aug 2017
Externally published	Yes

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https://arxiv.org/pdf/1307.0234.pdf

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title = "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 [6] 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.",

author = "Alessio Figalli and Enrico Valdinoci",

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AU - Valdinoci, Enrico

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AB - 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 [6] 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.

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U2 - 10.1515/crelle-2015-0006

DO - 10.1515/crelle-2015-0006

M3 - Article

SN - 0075-4102

VL - 2017

SP - 263

EP - 273

JO - Journal fur die Reine und Angewandte Mathematik

JF - Journal fur die Reine und Angewandte Mathematik

IS - 729

ER -

Regularity and Bernstein-type results for nonlocal minimal surfaces

Abstract

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