Let $U\subset\mathbb R^n$ be a bounded [open set](/page/Open%20Set), let $1\le p<\infty$, and let $u_0\in W^{1,p}(U)$. Let $F:\bar U\times\mathbb R\times\mathbb R^n\to[0,\infty)$ be continuous. Suppose that there is a constant $C<\infty$ such that, for every $(x,z,\xi)\in U\times\mathbb R\times\mathbb R^n$,