University of Oulu

Harjulehto Petteri, Hästö Peter: Boundary Regularity under Generalized Growth Conditions. Z. Anal. Anwend. 38 (2019), 73-96. doi: 10.4171/ZAA/1628

Boundary regularity under generalized growth conditions

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Author: Harjulehto, Petteri1; Hästö, Peter1,2
Organizations: 1University of Turku, Finland
2University of Oulu, Finland
Format: article
Version: accepted version
Access: open
Online Access: PDF Full Text (PDF, 0.5 MB)
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Language: English
Published: European Mathematical Society Publishing House, 2019
Publish Date: 2019-04-01


We study the Dirichlet ϕ-energy integral with Sobolev boundary values. The function ϕ has generalized Orlicz growth. Special cases include variable exponent and double phase growths. We show that minimizers are regular at the boundary provided a weak capacity fatness condition is satisfied. This condition is satisfied for instance if the boundary is Lipschitz. The results are new even for Orlicz spaces.

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Series: Zeitschrift für Analysis und ihre Anwendungen
ISSN: 0232-2064
ISSN-E: 1661-4534
ISSN-L: 0232-2064
Volume: 38
Issue: 1
Pages: 73 - 96
DOI: 10.4171/ZAA/1628
Type of Publication: A1 Journal article – refereed
Field of Science: 111 Mathematics
Copyright information: © 2019 EMS Publishing House. All rights reserved.