A Bernstein-type result for the minimal surface equation

Type:
Site:
Date:
21/03/2016 - 14:00 - 15:00
Salle:
421
Orateur:
FARINA Alberto
Localisation:
Université d'Amiens
Localisation:
France
Résumé:

We prove the following Bernstein-type theorem: if $u$ is an entire solution to the minimal surface equation, such that $N-1$ partial derivatives $\frac{\partial u}{\partial x_j}$ are bounded on one side (not necessarily the same), then $u$ is an affine function. Besides its novelty, our theorem also provides a new, simple and self-contained proof of celebrated results of Moser and of Bombieri-Giusti.