The General Theory of Homogenization

A Personalized Introduction

  • Luc Tartar

Part of the Lecture Notes of the Unione Matematica Italiana book series (UMILN, volume 7)

Table of contents

  1. Front Matter
    Pages i-xxii
  2. Luc Tartar
    Pages 1-21
  3. Luc Tartar
    Pages 89-95
  4. Luc Tartar
    Pages 97-103
  5. Luc Tartar
    Pages 105-112
  6. Luc Tartar
    Pages 113-127
  7. Luc Tartar
    Pages 129-136
  8. Luc Tartar
    Pages 137-145
  9. Luc Tartar
    Pages 147-155
  10. Luc Tartar
    Pages 157-165
  11. Luc Tartar
    Pages 167-175
  12. Luc Tartar
    Pages 177-183
  13. Luc Tartar
    Pages 185-194
  14. Luc Tartar
    Pages 195-202
  15. Luc Tartar
    Pages 203-209

About this book

Introduction

Homogenization is not about periodicity, or Gamma-convergence, but about understanding which effective equations to use at macroscopic level, knowing which partial differential equations govern mesoscopic levels, without using probabilities (which destroy physical reality); instead, one uses various topologies of weak type, the G-convergence of Sergio Spagnolo, the H-convergence of François Murat and the author, and some responsible for the appearance of nonlocal effects, which many theories in continuum mechanics or physics guessed wrongly.

For a better understanding of 20th century science, new mathematical tools must be introduced, like the author’s H-measures, variants by Patrick Gérard, and others yet to be discovered.

Keywords

H-measures compactness continuum mechanics differential equation homogenization partial differential equations physics

Authors and affiliations

  • Luc Tartar
    • 1
  1. 1.Dept. Mathematical SciencesCarnegie Mellon UniversityPittsburghUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-05195-1
  • Copyright Information Springer-Verlag Berlin Heidelberg 2010
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-642-05194-4
  • Online ISBN 978-3-642-05195-1
  • Series Print ISSN 1862-9113
  • About this book