Higher integrability for variational integrals with non-standard growth

Abstract

We consider autonomous integral functionals of the form F[u]:=∫Ωf(Du)dx where u:Ω→RN,N≥1,

where the convex integrand f satisfies controlled (p, q)-growth conditions. We establish higher gradient integrability and partial regularity for minimizers of F assuming qp<1+2n−1, n≥3. This improves earlier results valid under the more restrictive assumption qp<1+2n.