[Authors]
 Meshkova, Yu. M.; Suslina, T. A.

[Title]
 Homogenization for solutions of the Dirichlet problem for elliptic systems:
 Two-parametric error estimates

[AMS Subj-class]
 35B27 Homogenization; partial differential equations in media with periodic
       structure

[Abstract]
 Let $\mathcal{O}\subset\mathbb{R}^d$ be a bounded domain of class $C^{1,1}$.
 In $L_2(\mathcal{O};\mathbb{C}^n)$, we consider a selfadjoint matrix elliptic
 second order differential operator $B_{D,\varepsilon}$,
 $0<\varepsilon\leqslant1$, with the Dirichlet boundary condition.
 The principal part of the operator is given in a factorized form. The operator
 contains lower order terms with unbounded coefficients. The coefficients of
 $B_{D,\varepsilon}$ are periodic and depend on $\mathbf{x}/\varepsilon$. 
 We study the generalized resolvent
 $\left(B_{D,\varepsilon}-\zeta Q_0(\cdot/\varepsilon)\right)^{-1}$, 
 where $Q_0$ is a periodic bounded and positive definite matrix-valued function,
 and $\zeta$ is a complex parameter. 
 We obtain approximations for the generalized resolvent in the
 $L_2(\mathcal{O};\mathbb{C}^n)$-operator norm and in the norm of operators
 acting from $L_2(\mathcal{O};\mathbb{C}^n)$ to the Sobolev space
 $H^1(\mathcal{O};\mathbb{C}^n)$, with two-parametric error estimates
 (depending on $\varepsilon$ and $\zeta$).

[Keywords]
 periodic differential operators, elliptic systems, homogenization,
 operator error estimates

[Comments]
 LaTeX, Russian, 94 pp.

[Contact e-mail]
 suslina@list.ru