Homogenization Estimates of Nondivergence Elliptic Operators of Second Order

M. M. Sirazhudinov<sup>ab

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

Abstract: Questions related to the homogenization of the Dirichlet problem for nondivergence elliptic equations of second order with rapidly oscillating $\varepsilon$-periodic coefficients are studied. Error estimates of homogenization in the Sobolev spaces of order $\sqrt\varepsilon$ are obtained. Asymptotic homogenization methods are applied.

Keywords: elliptic operators, homogenization.

UDC: 517.956.2

Received: 07.05.2018
Revised: 18.11.2019

DOI: 10.4213/mzm12614

 English version: Mathematical Notes, 2020, 108:2, 250–271

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