# On the regularity of minimizers for scalar integral functionals with $(p,q)$-growth

## TL;DR

This paper improves the understanding of regularity for minimizers of scalar integral functionals with $(p,q)$-growth, establishing Lipschitz regularity under a new condition that extends previous results.

## Contribution

It proves Lipschitz regularity for minimizers under a less restrictive $(p,q)$-growth condition, advancing classical regularity results.

## Key findings

- Lipschitz regularity is established for minimizers when q/p<1+2/(n-1) for n≥3.
- The result extends previous regularity conditions by relaxing growth constraints.
- The paper refines the theoretical understanding of regularity in scalar integral functionals.

## Abstract

We revisit the question of regularity for minimizers of scalar autonomous integral functionals with so-called $(p,q)$-growth. In particular, we establish Lipschitz regularity under the condition $\frac{q}p<1+\frac{2}{n-1}$ for $n\geq3$ which improves a classical result due to Marcellini~[JDE'91].