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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 11 scientific papers (total in 11 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 (11)
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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
Russian version:
Matematicheskii Sbornik, 2014, Volume 205, Number 10, Pages 125–160
DOI: https://doi.org/10.4213/sm8364
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”, Mat. Sb., 205:10 (2014), 125–160; Sb. Math., 205:10 (2014), 1492–1527
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/sm/v205/i10/p125
    • This publication is cited in the following 11 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Abstract page:570
    Russian version PDF:296
    English version PDF:11
    References:103
    First page:43
     
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