Email this article Error Estimates of Homogenization in the Neumann Boundary Problem for an Elliptic Equation with Multiscale Coefficients
- Authors: Pastukhova S.E.1, Tikhomirov R.N.2
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Affiliations:
- Moscow State Institute of Radio Engineering, Electronics and Automation (Technical University)
- A. G. and N. G. Stoletov Vladimir State University
- Issue: Vol 216, No 2 (2016)
- Pages: 325-344
- Section: Article
- URL: https://journal-vniispk.ru/1072-3374/article/view/237802
- DOI: https://doi.org/10.1007/s10958-016-2903-1
- ID: 237802
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Abstract
We study the Neumann problem in a bounded domain Ω for a scalar elliptic equation with coefficients oscillating with respect to two groups of variables with periods of different smallness order. We prove the H1- and L2-estimates of homogenization. The estimates have the operator form and can be expressed in terms of the resolvent of the original problem and its approximations in the operator (L2(Ω)→H1(Ω))- and (L2(Ω)→L2(Ω))- norms.
About the authors
S. E. Pastukhova
Moscow State Institute of Radio Engineering, Electronics and Automation (Technical University)
Author for correspondence.
Email: pas-se@yandex.ru
Russian Federation, 78, pr. Vernadskogo, Moscow, 119454
R. N. Tikhomirov
A. G. and N. G. Stoletov Vladimir State University
Email: pas-se@yandex.ru
Russian Federation, 87, ul. Gor’kogo, Vladimir, 600000
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