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

A Bernstein Type Theorem for Minimal Graphs over Convex Domains