{"title":"BIFURCATION STRUCTURE TO SERRIN’S OVERDETERMINED PROBLEM","authors":"Guowei Dai, Fang Liu, Qingbo Liu","doi":"10.1216/rmj.2023.53.1445","DOIUrl":null,"url":null,"abstract":"We study the bifurcation structure to Serrin’s overdetermined problem such that −Δu=1 in Ω, u=0, ∂νu= const on ∂Ω. We prove that the bifurcation from the straight cylinder Bλ1×ℝ with λ1>0 is critical at the bifurcation point. Moreover, we obtain the global structure of bifurcation branches. To study the global structure of bifurcation branches, we establish a global bifurcation theorem in finite dimensional space.","PeriodicalId":49591,"journal":{"name":"Rocky Mountain Journal of Mathematics","volume":"93 1","pages":"0"},"PeriodicalIF":0.7000,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Rocky Mountain Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1216/rmj.2023.53.1445","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We study the bifurcation structure to Serrin’s overdetermined problem such that −Δu=1 in Ω, u=0, ∂νu= const on ∂Ω. We prove that the bifurcation from the straight cylinder Bλ1×ℝ with λ1>0 is critical at the bifurcation point. Moreover, we obtain the global structure of bifurcation branches. To study the global structure of bifurcation branches, we establish a global bifurcation theorem in finite dimensional space.
期刊介绍：
Rocky Mountain Journal of Mathematics publishes both research and expository articles in mathematics, and particularly invites well-written survey articles.
The Rocky Mountain Journal of Mathematics endeavors to publish significant research papers and substantial expository/survey papers in a broad range of theoretical and applied areas of mathematics. For this reason the editorial board is broadly based and submissions are accepted in most areas of mathematics.
In addition, the journal publishes specialized conference proceedings.
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