{"title":"一类带mems算子的超定特征值问题","authors":"Saïma KHENISSY, IBRAHIM ZOUHIR","doi":"10.59277/mrar.2023.25.75.3.365","DOIUrl":null,"url":null,"abstract":"We consider an overdetermined eigenvalue problem related to the MEMS operator given by Lτ := ∆2 − τ∆ on a smooth bounded domain Ω ⊂ R N , N ≥ 2. We give radial solutions on balls. Moreover, we establish a symmetry result with respect to operator Lτ , that is, under some hypotheses, we show that if a solution does exist to the overdetermined eigenvalue problem, then the domain Ω must be a ball.","PeriodicalId":49858,"journal":{"name":"Mathematical Reports","volume":"13 1","pages":"0"},"PeriodicalIF":0.2000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On an overdetermined eigenvalue problem with mems operator\",\"authors\":\"Saïma KHENISSY, IBRAHIM ZOUHIR\",\"doi\":\"10.59277/mrar.2023.25.75.3.365\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We consider an overdetermined eigenvalue problem related to the MEMS operator given by Lτ := ∆2 − τ∆ on a smooth bounded domain Ω ⊂ R N , N ≥ 2. We give radial solutions on balls. Moreover, we establish a symmetry result with respect to operator Lτ , that is, under some hypotheses, we show that if a solution does exist to the overdetermined eigenvalue problem, then the domain Ω must be a ball.\",\"PeriodicalId\":49858,\"journal\":{\"name\":\"Mathematical Reports\",\"volume\":\"13 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.2000,\"publicationDate\":\"2023-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematical Reports\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.59277/mrar.2023.25.75.3.365\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Reports","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.59277/mrar.2023.25.75.3.365","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
摘要
我们考虑与光滑有界域上Lτ:=∆2−τ∆给出的MEMS算子相关的一个过定特征值问题Ω∧R N, N≥2。我们给出了球的径向解。此外，我们建立了一个关于Lτ算子的对称结果，即在某些假设下，我们证明了如果超定特征值问题的解存在，那么定义域Ω一定是一个球。
On an overdetermined eigenvalue problem with mems operator
We consider an overdetermined eigenvalue problem related to the MEMS operator given by Lτ := ∆2 − τ∆ on a smooth bounded domain Ω ⊂ R N , N ≥ 2. We give radial solutions on balls. Moreover, we establish a symmetry result with respect to operator Lτ , that is, under some hypotheses, we show that if a solution does exist to the overdetermined eigenvalue problem, then the domain Ω must be a ball.
期刊介绍：
The journal MATHEMATICAL REPORTS (formerly STUDII SI CERCETARI MATEMATICE) was founded in 1948 by the Mathematics Section of the Romanian Academy. It appeared under its first name until 1998 and received the name of Mathematical Reports in 1999. It is now published in one volume a year, consisting in 4 issues. The current average total number of pages is 500.
Our journal MATHEMATICAL REPORTS publishes original mathematical papers, written in English. Excellent survey articles may be also accepted. The editors will put strong emphasis on originality, quality and applicability.
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