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Spectral Problems in Homogenization Theory

  • V. V. Jikov
  • S. M. Kozlov
  • O. A. Oleinik

Abstract

The behavior of eigenvalues and eigenfunctions of the boundary value problems considered in the preceding chapters is studied here in the context of the homogenization theory. Our analysis is primarily based on the theorems (proved in Section 11.1) about spectral properties of a sequence of abstract operators. Direct application of these theorems allows us to describe asymptotic properties of eigenvalues and eigenfunctions for a wide class of boundary value problems with a small parameter which arise in the homogenization theory of differential operators.

Keywords

Elliptic Operator Spectral Problem Convolution Operator Homogenization Theory Stratify Medium 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • V. V. Jikov
    • 1
  • S. M. Kozlov
    • 2
  • O. A. Oleinik
    • 3
  1. 1.Department of MathematicsPedagogical Institute of VladimirVladimirRussia
  2. 2.Université Aix-Provence IMarseilleFrance
  3. 3.Department of Mathematics and MechanicsMoscow State UniversityMoscowRussia

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