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Calculus of Variations and Partial Differential Equations

Topics on Geometrical Evolution Problems and Degree Theory

  • Luigi Ambrosio
  • Norman Dancer
  • Giuseppe Buttazzo
  • Antonio Marino
  • M. K. V. Murthy

Table of contents

  1. Front Matter
    Pages I-IX
  2. Geometric Evolution Problems

    1. Front Matter
      Pages 1-1
    2. Luigi Ambrosio, Norman Dancer, Giuseppe Buttazzo, Antonio Marino, M. K. V. Murthy
      Pages 3-4
  3. Degree Theory on Convex Sets and Applications to Bifurcation

    1. Front Matter
      Pages 181-181
    2. Luigi Ambrosio, Norman Dancer, Giuseppe Buttazzo, Antonio Marino, M. K. V. Murthy
      Pages 183-184
    3. V. Benci, D. Fortunato
      Pages 259-283
  4. Back Matter
    Pages 327-347

About this book

Introduction

The link between Calculus of Variations and Partial Differential Equations has always been strong, because variational problems produce, via their Euler-Lagrange equation, a differential equation and, conversely, a differential equation can often be studied by variational methods. At the summer school in Pisa in September 1996, Luigi Ambrosio and Norman Dancer each gave a course on a classical topic (the geometric problem of evolution of a surface by mean curvature, and degree theory with applications to pde's resp.), in a self-contained presentation accessible to PhD students, bridging the gap between standard courses and advanced research on these topics. The resulting book is divided accordingly into 2 parts, and nicely illustrates the 2-way interaction of problems and methods. Each of the courses is augmented and complemented by additional short chapters by other authors describing current research problems and results.

Keywords

Calculus of Variations Lagrangian mechanics direct variational methods geometric measure theory partial differential equation partial differential equations topological variational methods

Authors and affiliations

  • Luigi Ambrosio
    • 1
  • Norman Dancer
    • 2
  1. 1.Scuola Normale SuperiorePisaItaly
  2. 2.School of MathematicsUniversity of SydneySydneyAustralia

Editors and affiliations

  • Giuseppe Buttazzo
    • 1
  • Antonio Marino
    • 1
  • M. K. V. Murthy
    • 1
  1. 1.Dipartimento di MatematicaUniversità di PisaPisaItaly

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-57186-2
  • Copyright Information Springer-Verlag Berlin Heidelberg 2000
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-64803-1
  • Online ISBN 978-3-642-57186-2
  • Buy this book on publisher's site