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Author: Figalli, Alessio × Subject: s-minimal surfaces ×

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    Regularity and Bernstein-type results for nonlocal minimal surfaces
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Figalli, Alessio; Valdinoci, Enrico
    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 [5] stating that the validity of Bernsteins theorem in dimension n + 1 is a consequence of the nonexistence of n-dimensional singular minimal cones in IRn.