This article is cited in 5 papers

An asymptotic method for homogenization for generalized Beltrami operators

M. M. Sirazhudinov<sup>ab

a</sup> Daghestan Scientific Centre of Russian Academy of Sciences, Makhachkala
^b Daghestan State University, Makhachkala

Abstract: Questions on the homogenization of the Riemann-Hilbert problem for the generalized Beltrami equation with rapidly oscillating periodic coefficients (with small period $\varepsilon$) are considered. Estimates of order $\sqrt\varepsilon$ are obtained for the homogenization error in Lebesgue and Sobolev spaces. Asymptotic methods of homogenization are used.
Bibliography: 16 titles.

Keywords: Beltrami's equation, homogenization, asymptotic methods.

UDC: 517.946

MSC: 30G20, 35B27

Received: 23.05.2016 and 14.09.2016

DOI: 10.4213/sm8742

 English version: Sbornik: Mathematics, 2017, 208:4, 546–567

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