Bernstein theorem for minimal graphs
= Bernstein theorem for minimal graphs
{c}
{title2=$1\leq n\leq7,\quad u\in C^2(\mathbb R^n),\quad\operatorname{div}\frac{Du}{\sqrt{1+|Du|^2}}=0\ \Longrightarrow\ u(x)=a\cdot x+b$}
Every entire classical minimal graph over $\mathbb R^n$ is affine for $1\leq n\leq7$. The dimension restriction is essential. This theorem applies to the <minimal surface equation for a graph>, without assuming a global bound on its gradient.
// Target: analysis.bigb