{"title":"多维锥体中的伪微分方程和边值问题","authors":"V. B. Vasil’ev","doi":"10.1134/s0012266123120091","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We consider a special boundary value problem in the Sobolev–Slobodetskii space for a\nmodel elliptic pseudodifferential equation in a multidimensional cone. Taking into account the\nspecial factorization of the elliptic symbol, we write the general solution of the pseudodifferential\nequation that contains an arbitrary function. To determine it unambiguously, some integral\ncondition is added to the equation, which makes it possible to write the solution in Fourier\ntransforms.\n</p>","PeriodicalId":50580,"journal":{"name":"Differential Equations","volume":"14 1","pages":""},"PeriodicalIF":0.8000,"publicationDate":"2024-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Pseudodifferential Equations and Boundary Value Problems in a Multidimensional Cone\",\"authors\":\"V. B. Vasil’ev\",\"doi\":\"10.1134/s0012266123120091\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<h3 data-test=\\\"abstract-sub-heading\\\">Abstract</h3><p> We consider a special boundary value problem in the Sobolev–Slobodetskii space for a\\nmodel elliptic pseudodifferential equation in a multidimensional cone. Taking into account the\\nspecial factorization of the elliptic symbol, we write the general solution of the pseudodifferential\\nequation that contains an arbitrary function. To determine it unambiguously, some integral\\ncondition is added to the equation, which makes it possible to write the solution in Fourier\\ntransforms.\\n</p>\",\"PeriodicalId\":50580,\"journal\":{\"name\":\"Differential Equations\",\"volume\":\"14 1\",\"pages\":\"\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2024-02-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Differential Equations\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1134/s0012266123120091\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Differential Equations","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1134/s0012266123120091","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
Pseudodifferential Equations and Boundary Value Problems in a Multidimensional Cone
Abstract
We consider a special boundary value problem in the Sobolev–Slobodetskii space for a
model elliptic pseudodifferential equation in a multidimensional cone. Taking into account the
special factorization of the elliptic symbol, we write the general solution of the pseudodifferential
equation that contains an arbitrary function. To determine it unambiguously, some integral
condition is added to the equation, which makes it possible to write the solution in Fourier
transforms.
期刊介绍：
Differential Equations is a journal devoted to differential equations and the associated integral equations. The journal publishes original articles by authors from all countries and accepts manuscripts in English and Russian. The topics of the journal cover ordinary differential equations, partial differential equations, spectral theory of differential operators, integral and integral–differential equations, difference equations and their applications in control theory, mathematical modeling, shell theory, informatics, and oscillation theory. The journal is published in collaboration with the Department of Mathematics and the Division of Nanotechnologies and Information Technologies of the Russian Academy of Sciences and the Institute of Mathematics of the National Academy of Sciences of Belarus.
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