Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2020
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2005.05115 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
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 $\frac{q}p<1+\frac2{n}$.