Brief Communications

Functional Analysis and Its Applications

, Volume 46, Issue 3, pp 234-238

First online:

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

  • T. A. SuslinaAffiliated withDepartment of Physics, St. Petersburg State University Email author 

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access


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