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

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 $n\ge 3$ which improves a classical result due to Marcellini~[JDE'91].