Functional Analysis and Its Applications

, Volume 46, Issue 3, pp 234–238

Operator error estimates in L2 for homogenization of an elliptic dirichlet problem

Brief Communications

Abstract

In a bounded domain O ⊂ ℝd with C1,1 boundary a matrix elliptic second-order operator AD,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 AD0 is an effective operator with constant coefficients and Dirichlet boundary condition.

Key words

periodic differential operators homogenization effective operator operator error estimates 

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Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  1. 1.Department of PhysicsSt. Petersburg State UniversitySt. PetersburgRussia

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