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arXiv · 1904.12279

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

Peter Bella·Mathias Schäffner
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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].

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Peter Bella, Mathias Schäffner. 2019-04-28. On the regularity of minimizers for scalar integral functionals with $(p,q)$-growth. https://doi.org/10.2140/apde.2020.13.2241

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