{"title":"q-扭转刚度的Lp-Minkowski问题","authors":"Bin Chen, Xia Zhao, Weidong Wang, P. Zhao","doi":"10.1515/acv-2022-0041","DOIUrl":null,"url":null,"abstract":"Abstract In this paper, we introduce the L p {L_{p}} q-torsional measure for p ∈ ℝ {p\\in\\mathbb{R}} and q > 1 {q>1} by the L p {L_{p}} variational formula for the q-torsional rigidity of convex bodies without smoothness conditions. Moreover, we achieve the existence of solutions to the L p {L_{p}} Minkowski problem with respect to the q-torsional rigidity for discrete measures and general measures when 0 < p < 1 {0 1 {q>1} .","PeriodicalId":49276,"journal":{"name":"Advances in Calculus of Variations","volume":" ","pages":""},"PeriodicalIF":1.3000,"publicationDate":"2022-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The Lp Minkowski problem for q-torsional rigidity\",\"authors\":\"Bin Chen, Xia Zhao, Weidong Wang, P. Zhao\",\"doi\":\"10.1515/acv-2022-0041\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract In this paper, we introduce the L p {L_{p}} q-torsional measure for p ∈ ℝ {p\\\\in\\\\mathbb{R}} and q > 1 {q>1} by the L p {L_{p}} variational formula for the q-torsional rigidity of convex bodies without smoothness conditions. Moreover, we achieve the existence of solutions to the L p {L_{p}} Minkowski problem with respect to the q-torsional rigidity for discrete measures and general measures when 0 < p < 1 {0 1 {q>1} .\",\"PeriodicalId\":49276,\"journal\":{\"name\":\"Advances in Calculus of Variations\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":1.3000,\"publicationDate\":\"2022-05-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Advances in Calculus of Variations\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1515/acv-2022-0041\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Calculus of Variations","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1515/acv-2022-0041","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Abstract In this paper, we introduce the L p {L_{p}} q-torsional measure for p ∈ ℝ {p\in\mathbb{R}} and q > 1 {q>1} by the L p {L_{p}} variational formula for the q-torsional rigidity of convex bodies without smoothness conditions. Moreover, we achieve the existence of solutions to the L p {L_{p}} Minkowski problem with respect to the q-torsional rigidity for discrete measures and general measures when 0 < p < 1 {0 1 {q>1} .
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Advances in Calculus of Variations publishes high quality original research focusing on that part of calculus of variation and related applications which combines tools and methods from partial differential equations with geometrical techniques.
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