{"title":"On Dirichlet problem","authors":"A. K. Gushchin","doi":"10.1134/s0040577924010045","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> During almost two centuries after the Gauss’ formulation of the Dirichlet problem for Laplace equation, many famous mathematicians devoted their studies to this subject and to its various generalizations. Many interesting and important results have been obtained, which become already classical ones. Our paper is an extended presentation of the author’s talk on the international conference dedicate to the century of V. S. Vladimirov birthday. Its main content is the review of the results in that direction, including the proves of new statements and discussion of unsolved problems. Our goal is to convince readers that, in this “principal” problem of mathematical physics, we know far from everything even about the case of linear equation. There are many interesting and important unsolved problems in that direction. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Theoretical and Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1134/s0040577924010045","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
引用次数: 0
Abstract
During almost two centuries after the Gauss’ formulation of the Dirichlet problem for Laplace equation, many famous mathematicians devoted their studies to this subject and to its various generalizations. Many interesting and important results have been obtained, which become already classical ones. Our paper is an extended presentation of the author’s talk on the international conference dedicate to the century of V. S. Vladimirov birthday. Its main content is the review of the results in that direction, including the proves of new statements and discussion of unsolved problems. Our goal is to convince readers that, in this “principal” problem of mathematical physics, we know far from everything even about the case of linear equation. There are many interesting and important unsolved problems in that direction.
期刊介绍：
Theoretical and Mathematical Physics covers quantum field theory and theory of elementary particles, fundamental problems of nuclear physics, many-body problems and statistical physics, nonrelativistic quantum mechanics, and basic problems of gravitation theory. Articles report on current developments in theoretical physics as well as related mathematical problems.
Theoretical and Mathematical Physics is published in collaboration with the Steklov Mathematical Institute of the Russian Academy of Sciences.
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