Flatness results for nonlocal minimal cones and subgraphs

• Alberto Farina ^[1] ; Enrico Valdinoci ^[2]
  1. [1] University of Picardie Jules Verne

     University of Picardie Jules Verne

     Arrondissement d’Amiens, Francia

     
  2. [2] University of Western Australia

     University of Western Australia

     Australia

     
• Localización: Annali della Scuola Normale Superiore di Pisa. Classe di scienze, ISSN 0391-173X, Vol. 19, Nº 4, 2019, págs. 1281-1301
• Idioma: inglés
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• Resumen

  • We show that nonlocal minimal cones which are non-singular subgraphs outside the origin are necessarily halfspaces.

    The proof is based on classical ideas of [14] and on the computation of the linearized nonlocal mean curvature operator, which is proved to satisfy a suitable maximum principle.

    With this, we obtain new, and somehow simpler, proofs of the Bernsteintype results for nonlocal minimal surfaces which have been recently established in [20]. In addition, we establish a new nonlocal Bernstein-Moser-type result which classifies Lipschitz nonlocal minimal subgraphs outside a ball.