Let $U\subset\mathbb R^n$ be bounded and open, let $1<p<\infty$, and let $\mathcal A\subset W^{1,p}(U)$ be nonempty and sequentially weakly closed in $W^{1,p}(U)$. Assume that there exist constants $K_1,K_2\ge 0$ such that, for every $u\in\mathcal A$,
Let $f^{**}:\mathbb R^n\to\mathbb R$ be convex and lower semicontinuous. Suppose that there exist constants $c,C>0$ such that, for every $\xi\in\mathbb R^n$,