25 Gennaio, 2017 17:15 oclock

Sezione di Analisi

A Bernstein-type result for the minimal surface equation

Alberto Farina, Université Picardie Jules Verne

Aula seminari 6° piano

We prove the following Bernstein-type theorem: if $u$ is a solution to the minimal surface equation over $R^N$, such that $N-1$ partial derivatives 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 J. Moser and of E. Bombieri e E. Giusti.