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

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 ÌÄ-183.2014.1

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

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

Bibliographic databases:

UDC: 517.956+517.984
MSC: Primary 35J25; Secondary 47A10

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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• http://mi.mathnet.ru/eng/msb8364
• https://doi.org/10.4213/sm8364
• http://mi.mathnet.ru/eng/msb/v205/i10/p125

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Citing articles on Google Scholar: Russian citations, English citations
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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
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
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