Vol. 13, No. 7, 2020

Download this article
Download this article For screen
For printing
Recent Issues

Volume 14
Issue 6, 1671–1976
Issue 5, 1333–1669
Issue 4, 985–1332
Issue 3, 667–984
Issue 2, 323–666
Issue 1, 1–322

Volume 13, 8 issues

Volume 12, 8 issues

Volume 11, 8 issues

Volume 10, 8 issues

Volume 9, 8 issues

Volume 8, 8 issues

Volume 7, 8 issues

Volume 6, 8 issues

Volume 5, 5 issues

Volume 4, 5 issues

Volume 3, 4 issues

Volume 2, 3 issues

Volume 1, 3 issues

The Journal
About the Journal
Editorial Board
Editors’ Interests
Subscriptions
 
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
 
ISSN: 1948-206X (e-only)
ISSN: 2157-5045 (print)
Author Index
To Appear
 
Other MSP Journals
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