The Bernstein problem for elliptic functionals

Abstract: The Bernstein problem asks whether entire minimal graphs in $\mathbb{R}^{n+1}$ are necessarily hyperplanes. This problem was completely solved by the late 1960s in combined works of Bernstein, Fleming, De Giorgi, Almgren, Simons, and Bombieri-De Giorgi-Giusti. We will discuss the analogue of this problem for more general elliptic functionals, and some recent progress in the case n = 6.

analysis of PDEs

Audience: researchers in the topic

PDE seminar via Zoom