{"title":"变指数Sobolev空间中的一致凸性","authors":"Mostafa Bachar, Mohamed A. Khamsi, Osvaldo Méndez","doi":"10.3390/sym15111988","DOIUrl":null,"url":null,"abstract":"We prove the modular convexity of the mixed norm Lp(ℓ2) on the Sobolev space W1,p(Ω) in a domain Ω⊂Rn under the sole assumption that the exponent p(x) is bounded away from 1, i.e., we include the case supx∈Ωp(x)=∞. In particular, the mixed Sobolev norm is uniformly convex if 1<infx∈Ωp(x)≤supx∈Ωp(x)<∞ and W01,p(Ω) is uniformly convex.","PeriodicalId":48874,"journal":{"name":"Symmetry-Basel","volume":null,"pages":null},"PeriodicalIF":2.2000,"publicationDate":"2023-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Uniform Convexity in Variable Exponent Sobolev Spaces\",\"authors\":\"Mostafa Bachar, Mohamed A. Khamsi, Osvaldo Méndez\",\"doi\":\"10.3390/sym15111988\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We prove the modular convexity of the mixed norm Lp(ℓ2) on the Sobolev space W1,p(Ω) in a domain Ω⊂Rn under the sole assumption that the exponent p(x) is bounded away from 1, i.e., we include the case supx∈Ωp(x)=∞. In particular, the mixed Sobolev norm is uniformly convex if 1<infx∈Ωp(x)≤supx∈Ωp(x)<∞ and W01,p(Ω) is uniformly convex.\",\"PeriodicalId\":48874,\"journal\":{\"name\":\"Symmetry-Basel\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.2000,\"publicationDate\":\"2023-10-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Symmetry-Basel\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.3390/sym15111988\",\"RegionNum\":3,\"RegionCategory\":\"综合性期刊\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MULTIDISCIPLINARY SCIENCES\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Symmetry-Basel","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3390/sym15111988","RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MULTIDISCIPLINARY SCIENCES","Score":null,"Total":0}
Uniform Convexity in Variable Exponent Sobolev Spaces
We prove the modular convexity of the mixed norm Lp(ℓ2) on the Sobolev space W1,p(Ω) in a domain Ω⊂Rn under the sole assumption that the exponent p(x) is bounded away from 1, i.e., we include the case supx∈Ωp(x)=∞. In particular, the mixed Sobolev norm is uniformly convex if 1
期刊介绍:
Symmetry (ISSN 2073-8994), an international and interdisciplinary scientific journal, publishes reviews, regular research papers and short notes. Our aim is to encourage scientists to publish their experimental and theoretical research in as much detail as possible. There is no restriction on the length of the papers. Full experimental and/or methodical details must be provided, so that results can be reproduced.