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Elementary Soft and Stiff Problems

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

Abstract

For a large class of homogenization problems the given periodic matrix A(x) satisfies the usual inequality v1IA(x) ≤ v2I (v1, v2 > 0) at all points of ℝ m outside certain subsets, called inclusions, where the matrix A(x) is degenerate. Two main types of degeneration are usually considered: if A(x) = 0, then we speak of soft inclusions, or a soft problem; if, on the other hand, the inverse matrix B = 0, then we are dealing with stiff inclusions, or a stiff problem. As a rule, the matrix A(x) is constant outside the inclusions, and therefore we have a kind of two-phase periodic medium.

Keywords

Vector Field Dirichlet Problem Integral Identity Homogenize Matrix Virtual Mass 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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