, Volume 46, Issue 3, pp 234-238
Date: 14 Sep 2012

Operator error estimates in L 2 for homogenization of an elliptic dirichlet problem

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Abstract

In a bounded domain O ⊂ ℝd with C 1,1 boundary a matrix elliptic second-order operator A D,ɛ with Dirichlet boundary condition is studied. The coefficients of this operator are periodic and depend on x/ɛ, where ɛ s 0 is a small parameter. The sharp-order error estimate $$ \left\| {A_{D,\varepsilon }^{ - 1} - \left( {A_D^0 } \right)^{ - 1} } \right\|\left. {L_2 \to L_2 \leqslant C\varepsilon } \right| $$ is obtained. Here A D 0 is an effective operator with constant coefficients and Dirichlet boundary condition.

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Translated from Funktsional’nyi Analiz i Ego Prilozheniya, Vol. 46, No. 3, pp. 91–96, 2012
Original Russian Text Copyright © by T. A. Suslina
Supported by the RFBR (grant no. 11-01-00458-a) and the program “Leading Scientific Schools” (grant no. NSh-357.2012.1).