Grid generation via deformation (Q1195637)

The main Theorem is the following: Let \(V\subset R^ n\) be a bounded open set, \(f\in C^ K(\overline V)\) \({(f>0,}K\geq 1)\) and \(\int_ Vl/f(x)dx=| V|\). Then there exists \(u\in\text{Diff}^ K(\overline V)\) satisfying \[ \text{det}\nabla u(x)=f(u(x)),\quad x\in V,\quad u(x)=x,\quad x\in\partial V. \]