Functional Analysis and Its Applications

, Volume 46, Issue 3, pp 234–238

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

Authors

    • Department of PhysicsSt. Petersburg State University
Brief Communications

DOI: 10.1007/s10688-012-0031-3

Cite this article as:
Suslina, T.A. Funct Anal Its Appl (2012) 46: 234. doi:10.1007/s10688-012-0031-3

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.

Key words

periodic differential operators homogenization effective operator operator error estimates

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© Springer-Verlag 2012