University of Oulu

Harjulehto, P., Hästö, P. & Toivanen, O. Calc. Var. (2017) 56: 22.

Hölder regularity of quasiminimizers under generalized growth conditions

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Author: Harjulehto, Petteri1; Hästö, Peter1,2; Toivanen, Olli3
Organizations: 1Department of Mathematics and Statistics, University of Turku, Turku, Finland
2Department of Mathematics, University of Oulu, Oulu, Finland
3Institute of Mathematics, Polish Academy of Sciences, Warsaw, Poland
Format: article
Version: accepted version
Access: open
Online Access: PDF Full Text (PDF, 0.3 MB)
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Language: English
Published: Springer Nature, 2017
Publish Date: 2019-03-28


We prove Harnack’s inequality for local (quasi)minimizers in generalized Orlicz spaces without polynomial growth or coercivity conditions. As a consequence, we obtain the local Hölder continuity of local (quasi)minimizers. The results include as special cases standard, variable exponent and double phase growth.

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Series: Calculus of variations and partial differential equations
ISSN: 0944-2669
ISSN-E: 1432-0835
ISSN-L: 0944-2669
Volume: 56
Issue: 2
Article number: 22
DOI: 10.1007/s00526-017-1114-z
Type of Publication: A1 Journal article – refereed
Field of Science: 111 Mathematics
Copyright information: © Springer-Verlag Berlin Heidelberg 2017. This is a post-peer-review, pre-copyedit version of an article published in Calculus of Variations and Partial Differential Equations. The final authenticated version is available online at: