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 (p,q)-growth. In particular, we establish Lipschitz regularity under the condition q p < 1 + 2 n1 for n 3, improving a classical result due to Marcellini (J. Differential Equations 90:1 (1991), 1–30).

Keywords
nonuniformly elliptic equations, local Lipschitz continuity, $(p,q)$-growth, nonstandard growth conditions
Mathematical Subject Classification 2010
Primary: 35B65
Milestones
Received: 18 May 2019
Revised: 10 July 2019
Accepted: 6 September 2019
Published: 10 November 2020
Authors
Peter Bella
Fakultät für Mathematik
Technische Universität Dortmund
Dortmund
Germany
Mathias Schäffner
Mathematisches Institut
Universität Leipzig
Leipzig
Germany