Higher integrability for variational integrals with non-standard growth
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Date
2021-04-09
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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.