Bernstein theorem for minimal graphs ($1\le n\le 7,u\in C^2({\mathbb{R}}^n),\mathrm{div}\frac{Du}{\sqrt{1+|Du{|}^2}}=0⟹u(x)=a\cdot x+b$)

Every entire classical minimal graph over ${\mathbb{R}}^n$ is affine for $1\le n\le 7$. 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