{"title":"锥上狄利克雷问题产生的算子铅笔谱","authors":"V. Kozlov, V. Maz'ya","doi":"10.1070/SM1992V073N01ABEH002533","DOIUrl":null,"url":null,"abstract":"The operator pencil whose eigenvalues determine singularities of solutions to the Dirichlet problem at the vertex of a cone is studied. First the Dirichlet-Sobolev problem with data on the ray is considered, and the eigenvalues and eigenfunctions of the corresponding operator pencil are described. Then this information is used to show that the result of [2] is best possible in a sense.","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"37 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1992-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"19","resultStr":"{\"title\":\"ON THE SPECTRUM OF THE OPERATOR PENCIL GENERATED BY THE DIRICHLET PROBLEM IN A CONE\",\"authors\":\"V. Kozlov, V. Maz'ya\",\"doi\":\"10.1070/SM1992V073N01ABEH002533\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The operator pencil whose eigenvalues determine singularities of solutions to the Dirichlet problem at the vertex of a cone is studied. First the Dirichlet-Sobolev problem with data on the ray is considered, and the eigenvalues and eigenfunctions of the corresponding operator pencil are described. Then this information is used to show that the result of [2] is best possible in a sense.\",\"PeriodicalId\":208776,\"journal\":{\"name\":\"Mathematics of The Ussr-sbornik\",\"volume\":\"37 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1992-02-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"19\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematics of The Ussr-sbornik\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1070/SM1992V073N01ABEH002533\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematics of The Ussr-sbornik","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1070/SM1992V073N01ABEH002533","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
ON THE SPECTRUM OF THE OPERATOR PENCIL GENERATED BY THE DIRICHLET PROBLEM IN A CONE
The operator pencil whose eigenvalues determine singularities of solutions to the Dirichlet problem at the vertex of a cone is studied. First the Dirichlet-Sobolev problem with data on the ray is considered, and the eigenvalues and eigenfunctions of the corresponding operator pencil are described. Then this information is used to show that the result of [2] is best possible in a sense.
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