5 Dicembre, 2017 15:15

Sezione di Analisi

A sharp Bernstein-type theorem for entire minimal graphs

Alberto Farina, Université de Picardie

Sala Consiglio 7° piano

We consider entire solutions $u$ to the minimal surface equation in $R^N$, with $N\ge8$, and we prove the following sharp result : if $N-7$ partial derivatives $ \frac{\partial u }{\partial {x_j}}$ are bounded on one side (not necessarily the same), then $u$ is necessarily an affine function.