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 R-n.
Regularity and Bernstein-type results for nonlocal minimal surfaces / A. Figalli, E. Valdinoci. - In: JOURNAL FÜR DIE REINE UND ANGEWANDTE MATHEMATIK. - ISSN 0075-4102. - 729(2017 Aug), pp. 263-273. [10.1515/crelle-2015-0006]
Regularity and Bernstein-type results for nonlocal minimal surfaces
E. Valdinoci
2017
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 R-n.
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