{"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":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1134/s0012266123120091","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
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.
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