A Bernstein-type result for the minimal surface equation

• Alberto Farina ^[1]
  1. [1] University of Picardie Jules Verne

     University of Picardie Jules Verne

     Arrondissement d’Amiens, Francia

     
• Localización: Annali della Scuola Normale Superiore di Pisa. Classe di scienze, ISSN 0391-173X, Vol. 14, Nº 4, 2015, págs. 1231-1237
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • We prove the following Bernstein-type theorem: if u is an entire solution to the minimal surface equation, such that N − 1 partial derivatives ∂u/∂xj are bounded on one side (not necessarily the same), then u is an affine function.

    Its proof relies only on the Harnack inequality on minimal surfaces proved in [4] thus, besides its novelty, our theoremalso provides a new and self-contained proof of celebrated results of Moser and of Bombieri and Giusti.