Existence and regularity of minimizers of nonconvex integrals with

We show that local minimizers of functionals of the form $\int_{\Omega} \left[f(Du(x)) + g(x\,,u(x))\right]\,{\rm d}x$, $u \in u_0 + W_0^{1,p}(\Omega)$, are locally Lipschitz continuous provided f is a convex function with $p-q$ growth satisfying a condition of qualified convexity at infinity and g is Lipschitz continuous in u. As a consequence of this, we obtain an existence result for a related nonconvex functional