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Variational Methods in Mathematical Physics

A Unified Approach

  • Textbook
  • © 1992

Overview

Authors:
  1. Philippe Blanchard

    1. Theoretische Physik, Fakultät für Physik, Universität Bielefeld, Bielefeld, Germany

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  2. Erwin Brüning

    1. Department of Mathematics, University of Cape Town, Rondebosch, South Africa

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    You can also search for this author in PubMed   Google Scholar

Part of the book series: Theoretical and Mathematical Physics (TMP)

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Table of contents (11 chapters)

  1. Front Matter

    Pages I-XII
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  2. Some Remarks on the History and Objectives of the Calculus of Variations

    • Philippe Blanchard, Erwin Brüning
    Pages 1-14

  3. Direct Methods of the Calculus of Variations

    • Philippe Blanchard, Erwin Brüning
    Pages 15-34

  4. Differential Calculus in Banach Spaces

    • Philippe Blanchard, Erwin Brüning
    Pages 35-53

  5. Extrema of Differentiable Functions

    • Philippe Blanchard, Erwin Brüning
    Pages 54-62

  6. Constrained Minimisation Problems (Method of Lagrange Multipliers)

    • Philippe Blanchard, Erwin Brüning
    Pages 63-76

  7. Classical Variational Problems

    • Philippe Blanchard, Erwin Brüning
    Pages 77-141

  8. The Variational Approach to Linear Boundary and Eigenvalue Problems

    • Philippe Blanchard, Erwin Brüning
    Pages 142-170

  9. Nonlinear Elliptic Boundary Value Problems and Monotonic Operators

    • Philippe Blanchard, Erwin Brüning
    Pages 171-191

  10. Nonlinear Elliptic Eigenvalue Problems

    • Philippe Blanchard, Erwin Brüning
    Pages 192-240

  11. Semilinear Elliptic Differential Equations. Some Recent Results on Global Solutions

    • Philippe Blanchard, Erwin Brüning
    Pages 241-339

  12. Thomas-Fermi Theory

    • Philippe Blanchard, Erwin Brüning
    Pages 340-362

  13. Back Matter

    Pages 363-410
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Keywords

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).

Authors and Affiliations

  • Theoretische Physik, Fakultät für Physik, Universität Bielefeld, Bielefeld, Germany

    Philippe Blanchard

  • Department of Mathematics, University of Cape Town, Rondebosch, South Africa

    Erwin Brüning

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