A sharp Bernstein-type theorem for entire minimal graphs

Alberto Farina (1)

1 LAMFA - Laboratoire Amiénois de Mathématique Fondamentale et Appliquée - UMR CNRS 7352

We consider entire solutions u to the minimal surface equation in R-N, with N >= 8, and we prove the following sharp result: if N - 7 partial derivatives partial derivative u/partial derivative x(j) are bounded on one side (not necessarily the same), then u is necessarily an affine function.

Domaines: Mathématiques [math]

Alberto Farina. A sharp Bernstein-type theorem for entire minimal graphs. Calculus of Variations and Partial Differential Equations, 2018, 57 (5), ⟨10.1007/s00526-018-1392-0⟩. ⟨hal-03621411⟩