A1 Refereed original research article in a scientific journal
Boundary Regularity under Generalized Growth Conditions
Authors: Harjulehto P, Hästö P
Publisher: EUROPEAN MATHEMATICAL SOC
Publication year: 2019
Journal: Zeitschrift für Analysis und ihre Anwendungen
Journal name in source: ZEITSCHRIFT FUR ANALYSIS UND IHRE ANWENDUNGEN
Journal acronym: Z ANAL ANWEND
Volume: 38
Issue: 1
First page : 73
Last page: 96
Number of pages: 24
ISSN: 0232-2064
eISSN: 1661-4534
DOI: https://doi.org/10.4171/ZAA/1628
Abstract
We study the Dirichlet phi-energy integral with Sobolev boundary values. The function phi 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 satisfies for instance if the boundary is Lipschitz. The results are new even for Orlicz spaces.
We study the Dirichlet phi-energy integral with Sobolev boundary values. The function phi 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 satisfies for instance if the boundary is Lipschitz. The results are new even for Orlicz spaces.
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