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Mat. Sb., 2014, Volume 205, Number 10, Pages 125–160 (Mi msb8364)  

This article is cited in 2 scientific papers (total in 2 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

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


DOI: https://doi.org/10.4213/sm8364

Full text: PDF file (776 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2014, 205:10, 1492–1527

Bibliographic databases:

Document Type: Article
UDC: 517.956+517.984
MSC: Primary 35J25; Secondary 47A10
Received: 22.03.2014 and 26.07.2014

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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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. T. F. Sharapov, “On resolvent of multi-dimensional operators with frequent alternation of boundary conditions: critical case”, Ufa Math. J., 8:2 (2016), 65–94  mathnet  crossref  elib
    2. Chechkina A.G. D'Apice C. De Maio U., “Rate of Convergence of Eigenvalues to Singularly Perturbed Steklov-Type Problem For Elasticity System”, Appl. Anal., 98:1-2, SI (2019), 32–44  crossref  mathscinet  isi
  • Математический сборник Sbornik: Mathematics (from 1967)
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