Variational Methods in Mathematical Physics

A Unified Approach

  • Philippe Blanchard
  • Erwin Brüning

Part of the Texts and Monographs in Physics book series (TMP)

Table of contents

  1. Front Matter
    Pages I-XII
  2. Philippe Blanchard, Erwin Brüning
    Pages 1-14
  3. Philippe Blanchard, Erwin Brüning
    Pages 15-34
  4. Philippe Blanchard, Erwin Brüning
    Pages 35-53
  5. Philippe Blanchard, Erwin Brüning
    Pages 54-62
  6. Philippe Blanchard, Erwin Brüning
    Pages 63-76
  7. Philippe Blanchard, Erwin Brüning
    Pages 77-141
  8. Philippe Blanchard, Erwin Brüning
    Pages 142-170
  9. Philippe Blanchard, Erwin Brüning
    Pages 171-191
  10. Philippe Blanchard, Erwin Brüning
    Pages 192-240
  11. Philippe Blanchard, Erwin Brüning
    Pages 340-362
  12. Back Matter
    Pages 363-410

About this book


The first edition (in German) had the prevailing character of a textbook owing to the choice of material and the manner of its presentation. This second (translated, revised, and extended) edition, however, includes in its new parts considerably more recent and advanced results and thus goes partially beyond the textbook level. We should emphasize here that the primary intentions of this book are to provide (so far as possible given the restrictions of space) a selfcontained presentation of some modern developments in the direct methods of the cal­ culus of variations in applied mathematics and mathematical physics from a unified point of view and to link it to the traditional approach. These modern developments are, according to our background and interests: (i) Thomas-Fermi theory and related theories, and (ii) global systems of semilinear elliptic partial-differential equations and the existence of weak solutions and their regularity. Although the direct method in the calculus of variations can naturally be considered part of nonlinear functional analysis, we have not tried to present our material in this way. Some recent books on nonlinear functional analysis in this spirit are those by K. Deimling (Nonlinear Functional Analysis, Springer, Berlin Heidelberg 1985) and E. Zeidler (Nonlinear Functional Analysis and Its Applications, Vols. 1-4; Springer, New York 1986-1990).


Eigenvalue Funktionalanalyse Mathematische Physik Mechanik Quantenmechanik compactness functional analysis mathematical physics mechanics quantum mechanics

Authors and affiliations

  • Philippe Blanchard
    • 1
  • Erwin Brüning
    • 2
  1. 1.Theoretische Physik, Fakultät für PhysikUniversität BielefeldBielefeldGermany
  2. 2.Department of MathematicsUniversity of Cape TownRondeboschSouth Africa

Bibliographic information

  • DOI
  • Copyright Information Springer-Verlag Berlin Heidelberg 1992
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-82700-6
  • Online ISBN 978-3-642-82698-6
  • Series Print ISSN 1864-5879
  • Series Online ISSN 1864-5887
  • Buy this book on publisher's site