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This article is cited in 4 scientific papers (total in 4 papers)
The Neumann problem for elliptic equations with multiscale coefficients: operator estimates for homogenization
S. E. Pastukhova Moscow Technological University
Abstract:
We prove an $L^2$-estimate for the homogenization of an elliptic operator $A_\varepsilon$ in a domain $\Omega$ with a Neumann boundary condition on the boundary $\partial\Omega$. The coefficients of the operator $A_\varepsilon$ are rapidly oscillating over different groups of variables with periods of different orders of smallness as $\varepsilon\to 0$. We assume minimal regularity of the data, which makes it possible to impart to the result the meaning of an estimate in the operator $(L^2(\Omega)\to L^2(\Omega))$-norm for the difference of the resolvents of the original and homogenized problems. We also find an approximation to the resolvent of the original problem in the operator $(L^2(\Omega)\to H^1(\Omega))$-norm.
Bibliography: 24 titles.
Keywords:
multiscale homogenization, operator estimates for homogenization, Steklov smoothing.
Received: 04.02.2015 and 24.05.2015
Citation:
S. E. Pastukhova, “The Neumann problem for elliptic equations with multiscale coefficients: operator estimates for homogenization”, Sb. Math., 207:3 (2016), 418–443
Linking options:
https://www.mathnet.ru/eng/sm8486https://doi.org/10.1070/SM8486 https://www.mathnet.ru/eng/sm/v207/i3/p111
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Abstract page: | 539 | Russian version PDF: | 161 | English version PDF: | 24 | References: | 89 | First page: | 47 |
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