A Bernstein-type theorem for minimal graphs over convex domains

Abstract

Given any $n\ge 2$, we show that if $\Omega ⊊{\mathbb{R}}^n$ is an open convex domain (e.g. a half-space), and $u:\Omega \to \mathbb{R}$ is a solution to the minimal surface equation which agrees with a linear function on $\delta \Omega$, then $u$ must itself be linear.