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

Stein Compressibility CPIB 

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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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