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Bibliographic Details
Main Author: Schäffner, Mathias
Format: Preprint
Published: 2020
Subjects:
Online Access:https://arxiv.org/abs/2005.05115
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Table of Contents:
  • We consider autonomous integral functionals of the form $\mathcal F[u]:=\int_Ωf(D u)\,dx$ with $u:Ω\to\mathbb R^N$ $N\geq1$, 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 $\frac{q}p<1+\frac2{n-1}$, $n\geq3$. This improves earlier results valid under the more restrictive assumption $\frac{q}p<1+\frac2{n}$.