{"title":"Boundary Regularity under Generalized Growth Conditions","authors":"Petteri Harjulehto, P. Hästö","doi":"10.4171/ZAA/1628","DOIUrl":null,"url":null,"abstract":"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 satisfies for instance if the boundary is Lipschitz. The results are new even for Orlicz spaces.","PeriodicalId":54402,"journal":{"name":"Zeitschrift fur Analysis und ihre Anwendungen","volume":" ","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2019-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.4171/ZAA/1628","citationCount":"36","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Zeitschrift fur Analysis und ihre Anwendungen","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4171/ZAA/1628","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 36
Abstract
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 satisfies for instance if the boundary is Lipschitz. The results are new even for Orlicz spaces.
期刊介绍：
The Journal of Analysis and its Applications aims at disseminating theoretical knowledge in the field of analysis and, at the same time, cultivating and extending its applications.
To this end, it publishes research articles on differential equations and variational problems, functional analysis and operator theory together with their theoretical foundations and their applications – within mathematics, physics and other disciplines of the exact sciences.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
