{"title":"论椭圆域中适当椭圆方程迪里夏特问题的高效解法","authors":"A. H. Babayan, R. M. Veziryan","doi":"10.3103/s1068362324700018","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The fourth-order properly elliptic equation with multiple root is considered in the elliptic domain. The conditions, necessary and sufficient for the unique solvability of the Dirichlet problem for this equation are found, and if these conditions fail the defect numbers of this problem are determined. The solution of the problem is found in explicit form.</p>","PeriodicalId":54854,"journal":{"name":"Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences","volume":"46 1","pages":""},"PeriodicalIF":0.3000,"publicationDate":"2024-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On an Efficient Solution of the Dirichlet Problem for Properly Elliptic Equation in the Elliptic Domain\",\"authors\":\"A. H. Babayan, R. M. Veziryan\",\"doi\":\"10.3103/s1068362324700018\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<h3 data-test=\\\"abstract-sub-heading\\\">Abstract</h3><p>The fourth-order properly elliptic equation with multiple root is considered in the elliptic domain. The conditions, necessary and sufficient for the unique solvability of the Dirichlet problem for this equation are found, and if these conditions fail the defect numbers of this problem are determined. The solution of the problem is found in explicit form.</p>\",\"PeriodicalId\":54854,\"journal\":{\"name\":\"Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences\",\"volume\":\"46 1\",\"pages\":\"\"},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2024-04-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.3103/s1068362324700018\",\"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":"Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.3103/s1068362324700018","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
On an Efficient Solution of the Dirichlet Problem for Properly Elliptic Equation in the Elliptic Domain
Abstract
The fourth-order properly elliptic equation with multiple root is considered in the elliptic domain. The conditions, necessary and sufficient for the unique solvability of the Dirichlet problem for this equation are found, and if these conditions fail the defect numbers of this problem are determined. The solution of the problem is found in explicit form.
期刊介绍：
Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences) is an outlet for research stemming from the widely acclaimed Armenian school of theory of functions, this journal today continues the traditions of that school in the area of general analysis. A very prolific group of mathematicians in Yerevan contribute to this leading mathematics journal in the following fields: real and complex analysis; approximations; boundary value problems; integral and stochastic geometry; differential equations; probability; integral equations; algebra.
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