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- W2932316678 abstract "Let $mathcal{O}subsetmathbb{R}^d$ be a bounded domain of class $C^{1,1}$. In $L_2(mathcal{O};mathbb{C}^n)$, we study a selfadjoint matrix elliptic second order differential operator $B_{D,varepsilon}$, $0<varepsilonleqslant 1$, with the Dirichlet boundary condition. The principal part of the operator is given in a factorized form. The operator involves 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-valued 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 $zeta$)." @default.
- W2932316678 created "2019-04-11" @default.
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- W2932316678 date "2017-02-02" @default.
- W2932316678 modified "2023-09-27" @default.
- W2932316678 title "Homogenization of the Dirichlet problem for elliptic systems: Two-parametric error estimates" @default.
- W2932316678 hasPublicationYear "2017" @default.
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