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Homogenization of Differential Operators and Integral Functionals

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

Table of contents

  1. Front Matter
    Pages i-xi
  2. V. V. Jikov, S. M. Kozlov, O. A. Oleinik
    Pages 1-54
  3. V. V. Jikov, S. M. Kozlov, O. A. Oleinik
    Pages 55-85
  4. V. V. Jikov, S. M. Kozlov, O. A. Oleinik
    Pages 86-132
  5. V. V. Jikov, S. M. Kozlov, O. A. Oleinik
    Pages 133-148
  6. V. V. Jikov, S. M. Kozlov, O. A. Oleinik
    Pages 149-186
  7. V. V. Jikov, S. M. Kozlov, O. A. Oleinik
    Pages 187-221
  8. V. V. Jikov, S. M. Kozlov, O. A. Oleinik
    Pages 222-249
  9. V. V. Jikov, S. M. Kozlov, O. A. Oleinik
    Pages 250-297
  10. V. V. Jikov, S. M. Kozlov, O. A. Oleinik
    Pages 298-322
  11. V. V. Jikov, S. M. Kozlov, O. A. Oleinik
    Pages 338-366
  12. V. V. Jikov, S. M. Kozlov, O. A. Oleinik
    Pages 367-390
  13. V. V. Jikov, S. M. Kozlov, O. A. Oleinik
    Pages 391-414
  14. V. V. Jikov, S. M. Kozlov, O. A. Oleinik
    Pages 415-437
  15. V. V. Jikov, S. M. Kozlov, O. A. Oleinik
    Pages 438-459
  16. V. V. Jikov, S. M. Kozlov, O. A. Oleinik
    Pages 460-491
  17. V. V. Jikov, S. M. Kozlov, O. A. Oleinik
    Pages 492-501
  18. V. V. Jikov, S. M. Kozlov, O. A. Oleinik
    Pages 502-535
  19. Back Matter
    Pages 536-572

About this book

Introduction

It was mainly during the last two decades that the theory of homogenization or averaging of partial differential equations took shape as a distinct mathe­ matical discipline. This theory has a lot of important applications in mechanics of composite and perforated materials, filtration, disperse media, and in many other branches of physics, mechanics and modern technology. There is a vast literature on the subject. The term averaging has been usually associated with the methods of non­ linear mechanics and ordinary differential equations developed in the works of Poincare, Van Der Pol, Krylov, Bogoliubov, etc. For a long time, after the works of Maxwell and Rayleigh, homogeniza­ tion problems for· partial differential equations were being mostly considered by specialists in physics and mechanics, and were staying beyond the scope of mathematicians. A great deal of attention was given to the so called disperse media, which, in the simplest case, are two-phase media formed by the main homogeneous material containing small foreign particles (grains, inclusions). Such two-phase bodies, whose size is considerably larger than that of each sep­ arate inclusion, have been discovered to possess stable physical properties (such as heat transfer, electric conductivity, etc.) which differ from those of the con­ stituent phases. For this reason, the word homogenized, or effective, is used in relation to these characteristics. An enormous number of results, approximation formulas, and estimates have been obtained in connection with such problems as electromagnetic wave scattering on small particles, effective heat transfer in two-phase media, etc.

Keywords

Banach Space Functionals Maß Rang Variation differential equation diffusion extrema homogenization integral metric space partial differential equation probability probability space variational problem

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

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-84659-5
  • Copyright Information Springer-Verlag Berlin Heidelberg 1994
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-84661-8
  • Online ISBN 978-3-642-84659-5
  • Buy this book on publisher's site