{"title":"Dunkl-Laplacian算子的边值问题","authors":"M. Ben Chrouda, Khalifa El Mabrouk, Kods Hassine","doi":"10.19195/0208-4147.38.2.1","DOIUrl":null,"url":null,"abstract":"Let Δk be the Dunkl Laplacian on ℜd associated with a reflection group W and a multiplicity function k. The purpose of this paper is to establish the existence and the uniqueness of a positive solution on the unit ball B of ℜd to the following boundary value problem:Δku = φu in B and u = ƒ on ∂BWe distinguish two cases of nonnegative perturbation φ: trivial and nontrivial. ","PeriodicalId":48996,"journal":{"name":"Probability and Mathematical Statistics-Poland","volume":" ","pages":""},"PeriodicalIF":0.4000,"publicationDate":"2018-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Boundary value problems for the Dunkl Laplacian\",\"authors\":\"M. Ben Chrouda, Khalifa El Mabrouk, Kods Hassine\",\"doi\":\"10.19195/0208-4147.38.2.1\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let Δk be the Dunkl Laplacian on ℜd associated with a reflection group W and a multiplicity function k. The purpose of this paper is to establish the existence and the uniqueness of a positive solution on the unit ball B of ℜd to the following boundary value problem:Δku = φu in B and u = ƒ on ∂BWe distinguish two cases of nonnegative perturbation φ: trivial and nontrivial. \",\"PeriodicalId\":48996,\"journal\":{\"name\":\"Probability and Mathematical Statistics-Poland\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2018-12-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Probability and Mathematical Statistics-Poland\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.19195/0208-4147.38.2.1\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"STATISTICS & PROBABILITY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Probability and Mathematical Statistics-Poland","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.19195/0208-4147.38.2.1","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
Let Δk be the Dunkl Laplacian on ℜd associated with a reflection group W and a multiplicity function k. The purpose of this paper is to establish the existence and the uniqueness of a positive solution on the unit ball B of ℜd to the following boundary value problem:Δku = φu in B and u = ƒ on ∂BWe distinguish two cases of nonnegative perturbation φ: trivial and nontrivial.
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PROBABILITY AND MATHEMATICAL STATISTICS is published by the Kazimierz Urbanik Center for Probability and Mathematical Statistics, and is sponsored jointly by the Faculty of Mathematics and Computer Science of University of Wrocław and the Faculty of Pure and Applied Mathematics of Wrocław University of Science and Technology. The purpose of the journal is to publish original contributions to the theory of probability and mathematical statistics.
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