Lipschitz bounds for integral functionals with (p, q)-growth conditions

We study local regularity properties of local minimizers of scalar integral functionals of the form F[u] := integral(Omega) F(del u) - fu dx where the convex integrand F satisfies controlled (p, q)-growth conditions. We establish Lipschitz continuity under sharp assumptions on the forcing term f and improved assumptions on the growth conditions on F with respect to the existing literature. Along the way, we establish an L-infinity-L-2-estimate for solutions of linear uniformly elliptic equations in divergence form, which is optimal with respect to the ellipticity ratio of the coefficients.