Higher integrability for variational integrals with non-standard growth

Abstract

We consider autonomous integral functionals of the form $\mathcal{F}[u]:={\int }_{\Omega }f(Du)dx$ with $u:\Omega \to {\mathbb{R}}^N$ $N\ge 1$, where the convex integrand $f$ satisfies controlled $(p,q)$-growth conditions. We establish higher gradient integrability and partial regularity for minimizers of $\mathcal{F}$ assuming $\frac{q}{p}<1+\frac{2}{n-1}$, $n\ge 3$. This improves earlier results valid under the more restrictive assumption $\frac{q}{p}<1+\frac{2}{n}$.

13 pages

Cited by in corpus (2)

• Global higher integrability for minimisers of convex obstacle problems with (p,q)-growth
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