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Sbornik: Mathematics, 2014, Volume 205, Issue 10, Pages 1492–1527
DOI: https://doi.org/10.1070/SM2014v205n10ABEH004427 (Mi sm8364) 		 
This article is cited in 12 scientific papers (total in 12 papers)

On the resolvent of multidimensional operators with frequently changing boundary conditions in the case of the homogenized Dirichlet condition

T. F. Sharapov

Bashkir State Pedagogical University, Ufa
English version PDF (733 kB) Citations (12) Russian version article
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DOI: https://doi.org/10.1070/SM2014v205n10ABEH004427
Abstract: We consider an elliptic operator in a multidimensional domain with frequently changing boundary conditions in the case when the homogenized operator contains the Dirichlet boundary condition. We prove the uniform resolvent convergence of the perturbed operator to the homogenized operator and obtain estimates for the rate of convergence. A complete asymptotic expansion is constructed for the resolvent when it acts on sufficiently smooth functions.
Bibliography: 41 titles.
Keywords: frequent change, homogenization, uniform resolvent convergence, asymptotic behaviour.
Funding agency Grant number
Russian Foundation for Basic Research
Ministry of Education and Science of the Russian Federation МД-183.2014.1
Received: 22.03.2014 and 26.07.2014
Bibliographic databases:
Document Type: Article
UDC: 517.956+517.984
MSC: Primary 35J25; Secondary 47A10
Language: English
Original paper language: Russian
Citation: T. F. Sharapov, “On the resolvent of multidimensional operators with frequently changing boundary conditions in the case of the homogenized Dirichlet condition”, Sb. Math., 205:10 (2014), 1492–1527
Citation in format AMSBIB
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\vol 205
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  • https://doi.org/10.1070/SM2014v205n10ABEH004427
  • https://www.mathnet.ru/eng/sm/v205/i10/p125
    • This publication is cited in the following 12 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математический сборник Sbornik: Mathematics
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    Abstract page:595
    Russian version PDF:299
    English version PDF:13
    References:110
    First page:43
     
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