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.

Automated summary

In this paper, we study the local regularity properties of local minimizers of scalar integral functionals. We establish the Lipschitz continuity under sharp assumptions on the forcing term and improved assumptions on the growth conditions. We also provide an optimal L-infinity-L-2 estimate for solutions of linear uniformly elliptic equations.