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Geometric Analysis and Nonlinear Partial Differential Equations

  • Stefan Hildebrandt
  • Hermann Karcher

Table of contents

  1. Front Matter
    Pages I-IX
  2. Olga Ladyzhenskaya

    1. Michael Struwe
      Pages 1-10
  3. Geometric Analysis and Calculus of Variations

    1. Front Matter
      Pages 11-11
    2. Werner Ballmann, Jochen Brüning
      Pages 13-37
    3. Christian Bär, Sven Schopka
      Pages 39-67
    4. Friedrich Sauvigny
      Pages 105-115
    5. Matthias Weber
      Pages 117-127
    6. Konrad Polthier
      Pages 129-145
    7. W. Dörfler, K. G. Siebert
      Pages 147-175
    8. Ulrich Dierkes
      Pages 177-193
    9. Reiner Schätzte
      Pages 201-216
    10. Ulrich Clarenz, Gerhard Dziuk, Martin Rumpf
      Pages 217-248
    11. Frank Duzaar, Joseph F. Grotowski, Klaus Steffen
      Pages 265-296
    12. Stefan Hildebrandt, Heiko von der Mosel
      Pages 297-326
    13. Michael Bildhauer, Martin Fuchs
      Pages 327-344
  4. Nonlinear Partial Differential Equations

    1. Front Matter
      Pages 345-345
    2. Bernd Kirchheim, Stefan Müller, Vladimír Šverák
      Pages 347-395
    3. Thomas Kappeler, Jürgen Pöschel
      Pages 397-416
    4. Sebastian Noelle, Michael Westdickenberg
      Pages 417-430
    5. Sergio Albeverio, Yuri Kondratiev, Michael Röckner
      Pages 475-486
    6. Karl-Theodor Sturm
      Pages 487-504
    7. Carsten Ebmeyer, Jens Frehse, Moritz Kassmann
      Pages 505-517
    8. M. Griebel, M. A. Schweitzer
      Pages 519-542
    9. Harald Garcke, Stanislaus Maier-Paape, Ulrich Weikard
      Pages 603-635
    10. Roberta Dal Passo, Lorenzo Giacomelli, Günther Grün
      Pages 637-648
    11. Barbara Niethammer
      Pages 649-663
  5. Back Matter
    Pages 665-673

About this book

Introduction

This book is not a textbook, but rather a coherent collection of papers from the field of partial differential equations. Nevertheless we believe that it may very well serve as a good introduction into some topics of this classical field of analysis which, despite of its long history, is highly modem and well prospering. Richard Courant wrote in 1950: "It has always been a temptationfor mathematicians to present the crystallized product of their thought as a deductive general theory and to relegate the individual mathematical phenomenon into the role of an example. The reader who submits to the dogmatic form will be easily indoctrinated. Enlightenment, however, must come from an understanding of motives; live mathematical development springs from specific natural problems which can be easily understood, but whose solutions are difficult and demand new methods or more general significance. " We think that many, if not all, papers of this book are written in this spirit and will give the reader access to an important branch of analysis by exhibiting interest­ ing problems worth to be studied. Most of the collected articles have an extensive introductory part describing the history of the presented problems as well as the state of the art and offer a well chosen guide to the literature. This way the papers became lengthier than customary these days, but the level of presentation is such that an advanced graduate student should find the various articles both readable and stimulating.

Keywords

Kolmogorov–Arnold–Moser theorem differential equation geometric analysis nonlinear partial differential equation nonlinear partial differential equations partial differential equation

Editors and affiliations

  • Stefan Hildebrandt
    • 1
  • Hermann Karcher
    • 1
  1. 1.Department of MathematicsUniversity of BonnBonnGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-55627-2
  • Copyright Information Springer-Verlag Berlin Heidelberg 2003
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-44051-2
  • Online ISBN 978-3-642-55627-2
  • Buy this book on publisher's site