Regularity and Bernstein-type results for nonlocal minimal surfaces

Alessio Figalli, Enrico Valdinoci

Research output: Contribution to journalArticle

14 Citations (Scopus)

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 languageEnglish
Pages (from-to)263-273
JournalJournal fur die Reine und Angewandte Mathematik
Volume2017
Issue number729
Early online date1 Jan 2015
DOIs
Publication statusPublished - 28 Apr 2017
Externally publishedYes

Fingerprint

Minimal surface
Cones
Regularity
Theorem
Nonexistence
Lipschitz
n-dimensional
Cone

Cite this

@article{844c34cf245f44679d779a0c456d9c15,
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",
year = "2017",
month = "4",
day = "28",
doi = "10.1515/crelle-2015-0006",
language = "English",
volume = "2017",
pages = "263--273",
journal = "Journal fuer die Reine und Angewandte Mathematik: Crelle's journal",
issn = "0075-4102",
publisher = "Walter de Gruyter GmbH (European Journal of Nanomedicine)",
number = "729",

}

Regularity and Bernstein-type results for nonlocal minimal surfaces. / Figalli, Alessio; Valdinoci, Enrico.

In: Journal fur die Reine und Angewandte Mathematik, Vol. 2017, No. 729, 28.04.2017, p. 263-273.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Regularity and Bernstein-type results for nonlocal minimal surfaces

AU - Figalli, Alessio

AU - Valdinoci, Enrico

PY - 2017/4/28

Y1 - 2017/4/28

N2 - 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.

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.

UR - http://www.scopus.com/inward/record.url?scp=84990207903&partnerID=8YFLogxK

U2 - 10.1515/crelle-2015-0006

DO - 10.1515/crelle-2015-0006

M3 - Article

VL - 2017

SP - 263

EP - 273

JO - Journal fuer die Reine und Angewandte Mathematik: Crelle's journal

JF - Journal fuer die Reine und Angewandte Mathematik: Crelle's journal

SN - 0075-4102

IS - 729

ER -