# Homogenization of the Dirichlet problem for elliptic systems: Two-parametric error estimates

@article{Meshkova2017HomogenizationOT, title={Homogenization of the Dirichlet problem for elliptic systems: Two-parametric error estimates}, author={Yu. M. Meshkova and Tatiana Suslina}, journal={arXiv: Analysis of PDEs}, year={2017} }

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 study a selfadjoint matrix elliptic second order differential operator $B_{D,\varepsilon}$, $0<\varepsilon\leqslant 1$, 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…

## 6 Citations

Homogenization of the first initial boundary-value problem for parabolic systems: operator error estimates

- MathematicsSt. Petersburg Mathematical Journal
- 2018

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 second order elliptic differential operator…

Variations on the theme of the Trotter-Kato theorem for homogenization of periodic hyperbolic systems

- Mathematics, Computer Science
- 2019

The proof of the Trotter-Kato theorem is adopted by introduction of some correction term and hyperbolic results from elliptic ones are derived from elliptIC ones.

On homogenization of periodic hyperbolic systems in $L_2(\mathbb{R}^d;\mathbb{C}^n)$. Variations on the theme of the Trotter-Kato theorem

- Mathematics
- 2019

In L2(R d;Cn), we consider a matrix elliptic second order differential operator Bε > 0. Coefficients of the operator Bε are periodic with respect to some lattice in Rd and depend on x/ε. We study the…

Homogenization of the Neumann problem for higher order elliptic equations with periodic coefficients

- Mathematics
- 2017

Let be a bounded domain of class . In , we study a self-adjoint strongly elliptic operator of order 2p given by the expression , , with Neumann boundary conditions. Here, is a bounded and positive…

On homogenization of the first initial-boundary value problem for periodic hyperbolic systems

- MathematicsApplicable Analysis
- 2018

ABSTRACT Let be a bounded domain of class . In , we consider a self-adjoint matrix strongly elliptic second-order differential operator , , with the Dirichlet boundary condition. The coefficients of…

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