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

Bella, Peter; Schäffner, Mathias

doi:10.2140/apde.2020.13.2241

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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

DOI: 10.2140/apde.2020.13.2241

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 $n \geq 3$ , 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

Vol. 13, No. 7, 2020