{"title":"广义增长条件下的边界正则性","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":"{\"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}","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}
Boundary Regularity under Generalized Growth Conditions
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.
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