Homogenization of elliptic systems with periodic coefficients: operator error estimates in $L_2(\mathbb {R}^d)$ with corrector taken into account

DOI10.1090/spmj/1354zbMath1316.35024OpenAlexW2097890753MaRDI QIDQ5254801

Tatiana Suslina

Publication date: 10 June 2015

Published in: St. Petersburg Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/spmj/1354

zbMATH Keywords

correctoreffective operatoroperator error estimatesrapidly oscillating coefficientstwo-dimensional Pauli operator

Mathematics Subject Classification ID

Schrödinger operator, Schrödinger equation (35J10) Homogenization in context of PDEs; PDEs in media with periodic structure (35B27) Second-order elliptic systems (35J47)

Related Items (5)

On homogenization for non-self-adjoint periodic elliptic operators on an infinite cylinder ⋮ Variations on the theme of the Trotter-Kato theorem for homogenization of periodic hyperbolic systems ⋮ Homogenization of periodic Schrödinger-type equations, with lower order terms ⋮ Homogenization of periodic parabolic systems in the $L_2(\mathbb {R}^d)$-norm with the corrector taken into account ⋮ Homogenization of hyperbolic equations with periodic coefficients in ℝ^{𝕕}: Sharpness of the results

Cites Work

• On operator estimates for some problems in homogenization theory
• Some estimates from homogenization theory
• Approximation of the resolvent of a two-parametric quadratic operator pencil near the bottom of the spectrum
• Asymptotics for the solutions of elliptic systems with rapidly oscillating coefficients
• Homogenization in the Sobolev class $H^{1}(\mathbb R^{d})$ for second order periodic elliptic operators with the inclusion of first order terms
• Homogenization with corrector term for periodic elliptic differential operators
• Second order periodic differential operators. Threshold properties and homogenization
• Homogenization with corrector for periodic differential operators. Approximation of solutions in the Sobolev class $H^1({\mathbb{R}}^d)$
• Threshold approximations with corrector for the resolvent of a factorized selfadjoint operator family
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