# Homogenization for Non-self-adjoint Periodic Elliptic Operators on an Infinite Cylinder

@article{Senik2017HomogenizationFN,
title={Homogenization for Non-self-adjoint Periodic Elliptic Operators on an Infinite Cylinder},
author={Nikita N. Senik},
journal={SIAM J. Math. Anal.},
year={2017},
volume={49},
pages={874-898}
}
• N. N. Senik
• Published 20 August 2015
• Mathematics, Computer Science
• SIAM J. Math. Anal.
We consider the problem of homogenization for non-self-adjoint second-order elliptic differential operators~$\mathcal{A}^{\varepsilon}$ of divergence form on $L_{2}(\mathbb{R}^{d_{1}}\times\mathbb{T}^{d_{2}})$, where $d_{1}$ is positive and~$d_{2}$ is non-negative. The~coefficients of the operator~$\mathcal{A}^{\varepsilon}$ are periodic in the first variable with period~$\varepsilon$ and smooth in a certain sense in the second. We show that, as $\varepsilon$ gets small, $(\mathcal{A… 14 Citations Homogenization of the Dirichlet problem for elliptic systems: Two-parametric error estimates • Mathematics • 2017 Let$\mathcal{O}\subset\mathbb{R}^d$be a bounded domain of class$C^{1,1}$. In$L_2(\mathcal{O};\mathbb{C}^n)$, we study a selfadjoint matrix elliptic second order differential operator Homogenization for locally periodic elliptic problems on a domain Let$\Omega$be a Lipschitz domain in$\mathbb R^d$, and let$\mathcal A^\varepsilon=-\operatorname{div}A(x,x/\varepsilon)\nabla$be a strongly elliptic operator on$\Omega$. We suppose that Operator Estimates in Homogenization of Elliptic Systems of Equations We study homogenization of nonselfadjoint second order elliptic systems with ε-periodic rapidly oscillating coefficients as ε → 0. We obtain the L2- and H1-estimates for the homogenization error of On Resolvent Approximations of Elliptic Differential Operators with Locally Periodic Coefficients We study the asymptotic behaviour, as the small parameter$\varepsilon$tends to zero, of the resolvents of uniformly elliptic second-order differential operators with locally periodic coefficients Operator estimates for non-periodically perforated domains with Dirichlet and nonlinear Robin conditions: strange term . We consider a boundary value problem for a general second order linear equation in a domain with a ﬁne perforation. The latter is made by small cavities; both the shapes of the cavities and their Approximation of resolvents in homogenization of fourth-order elliptic operators We study the homogenization of a fourth-order divergent elliptic operator with rapidly oscillating -periodic coefficients, where is a small parameter. The homogenized operator is of the same type and On resolvent approximations of elliptic differential operators with periodic coefficients We consider resolvents ( A ϵ + 1 ) − 1 of elliptic second-order differential operators A ϵ = − div a ( x / ϵ ) ∇ in R d with e-periodic measurable matrix a ( x / ϵ ) and study the asymptotic beha... Norm convergence for problems with perforation along a given manifold with nonlinear Robin condition on boundaries of cavities • Economics • 2022 В работе рассматривается краевая задача для эллиптического уравнения второго порядка с переменными коэффициентами в многомерной области, перфорированной малыми полостями, часто расположенными вдоль ## References SHOWING 1-10 OF 22 REFERENCES OPERATOR ERROR ESTIMATES FOR HOMOGENIZATION OF THE ELLIPTIC DIRICHLET PROBLEM IN A BOUNDED DOMAIN • Mathematics • 2012 Let$\mathcal{O} \subset \mathbb{R}^d$be a bounded domain of class$C^2$. 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Spectral approach to homogenization of an elliptic operator periodic in some directions
• Mathematics
• 2011
The operatorvbox is considered in L2(ℝ2), where gj(x1, x2), j = 1, 2, are periodic in x1 with period 1, bounded and positive definite. Let function Q(x1, x2) be bounded, positive definite and