#### Vol. 13, No. 7, 2020

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

### Peter Bella and Mathias Schäffner

Vol. 13 (2020), No. 7, 2241–2257
##### Abstract

We revisit the question of regularity for minimizers of scalar autonomous integral functionals with so-called $\left(p,q\right)$-growth. In particular, we establish Lipschitz regularity under the condition $\frac{q}{p}<1+\frac{2}{n-1}$ for $n\ge 3$, improving a classical result due to Marcellini (J. Differential Equations 90:1 (1991), 1–30).

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nonuniformly elliptic equations, local Lipschitz continuity, $(p,q)$-growth, nonstandard growth conditions