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Russian Mathematical Surveys, 2016, Volume 71, Issue 3, Pages 417–511
DOI: https://doi.org/10.1070/RM9710 (Mi rm9710) 		 
This article is cited in 96 scientific papers (total in 96 papers)

Operator estimates in homogenization theory

V. V. Zhikova, S. E. Pastukhovab

a Vladimir State University
b Moscow Technological University (MIREA)
English version PDF (1201 kB) Citations (96)
References:
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DOI: https://doi.org/10.1070/RM9710
Abstract: This paper gives a systematic treatment of two methods for obtaining operator estimates: the shift method and the spectral method. Though substantially different in mathematical technique and physical motivation, these methods produce basically the same results. Besides the classical formulation of the homogenization problem, other formulations of the problem are also considered: homogenization in perforated domains, the case of an unbounded diffusion matrix, non-self-adjoint evolution equations, and higher-order elliptic operators.
Bibliography: 62 titles.
Keywords: shift method, integrated estimate, Steklov smoothing, periodicity, problem on the cell, asymptotics of the fundamental solution, spectral method, Bloch representation of an operator, Nash–Aronson estimate.
Funding agency Grant number
Russian Science Foundation 14-11-00398
This work was supported by the Russian Science Foundation under grant 14-11-00398.
Received: 21.12.2015
Russian version:
Uspekhi Matematicheskikh Nauk, 2016, Volume 71, Issue 3(429), Pages 27–122
DOI: https://doi.org/10.4213/rm9710
Bibliographic databases:
Document Type: Article
UDC: 517.97
MSC: Primary 35J15, 35K15, 35B27; Secondary 35J30
Language: English
Original paper language: Russian
Citation: V. V. Zhikov, S. E. Pastukhova, “Operator estimates in homogenization theory”, Uspekhi Mat. Nauk, 71:3(429) (2016), 27–122; Russian Math. Surveys, 71:3 (2016), 417–511
Citation in format AMSBIB
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    • This publication is cited in the following 96 articles:
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    References:122
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