Homogenization of the spectral Dirichlet problem for a system of differential equations with rapidly oscillating coefficients and changing sign density

DOI10.1007/S10958-010-0047-2zbMath1221.35258OpenAlexW2074077559MaRDI QIDQ548734

Sergueï A. Nazarov, Andrey L. Piatnitski

Publication date: 30 June 2011

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10958-010-0047-2

zbMATH Keywords

Dirichlet problemhomogenizationPDE with rapidly oscillating coefficients

Mathematics Subject Classification ID

General topics in linear spectral theory for PDEs (35P05) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30) Asymptotic expansions of solutions to PDEs (35C20) Homogenization in context of PDEs; PDEs in media with periodic structure (35B27) Second-order elliptic systems (35J47) Boundary value problems for second-order elliptic systems (35J57)

Related Items (5)

Homogenization of the Cauchy Problem for the Wave Equation with Rapidly Varying Coefficients and Initial Conditions ⋮ Spectrum of a diffusion operator with coefficient changing sign over a small inclusion ⋮ Homogenization of Steklov spectral problems with indefinite density function in perforated domains ⋮ Asymptotics of the Cauchy problem for the one-dimensional Schrödinger equation with rapidly oscillating initial data and small addition to the smooth potential ⋮ Homogenization of the spectral problem for periodic elliptic operators with sign-changing density function

Cites Work

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• Homogenization of elliptic eigenvalue problems. I
• Homogenization of eigenvalue problems in perforated domains
• Solvability in the small of nonstationary problems for incompressible ideal and viscous fluids and the case of vanishing viscosity
• Korn's inequality for periodic solids and convergence rate of homogenization
• The polynomial property of self-adjoint elliptic boundary-value problems and an algebraic description of their attributes

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