{"title":"Solution of a Boundary Value Problem for an Elliptic Equation with a Small Noninteger Order Degeneracy","authors":"D. P. Emel’yanov","doi":"10.1134/s0012266124030066","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We consider the Dirichlet boundary value problem for an elliptic type equation with\nirregular noninteger-order degeneration in a rectangle. The coefficients of the differential operator\nare supposed to be analytic. We construct a formal solution by using the method of spectral\nseparation of singularities in the form of a series; the character of the nonanalytic dependence of\nthe solution on the variable <span>\\(y\\)</span> in a neighborhood of\n<span>\\(y=0 \\)</span> is written out explicitly. We prove the convergence\nof the series to the classical solution using the Green’s function method.\n</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-07-08","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/s0012266124030066","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 the Dirichlet boundary value problem for an elliptic type equation with
irregular noninteger-order degeneration in a rectangle. The coefficients of the differential operator
are supposed to be analytic. We construct a formal solution by using the method of spectral
separation of singularities in the form of a series; the character of the nonanalytic dependence of
the solution on the variable \(y\) in a neighborhood of
\(y=0 \) is written out explicitly. We prove the convergence
of the series to the classical solution using the Green’s function method.
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