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Calculus of Variations and Partial Differential Equations

Topics on Geometrical Evolution Problems and Degree Theory

  • Textbook
  • © 2000

Overview

Authors:
  1. Luigi Ambrosio

    1. Scuola Normale Superiore, Pisa, Italy

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  2. Norman Dancer

    1. School of Mathematics, University of Sydney, Sydney, Australia

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Editors:
  1. Giuseppe Buttazzo

    1. Dipartimento di Matematica, Università di Pisa, Pisa, Italy

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  2. Antonio Marino

    1. Dipartimento di Matematica, Università di Pisa, Pisa, Italy

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  3. M. K. V. Murthy

    1. Dipartimento di Matematica, Università di Pisa, Pisa, Italy

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Table of contents (12 chapters)

  1. Front Matter

    Pages I-IX
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  2. Geometric Evolution Problems

    1. Front Matter

      Pages 1-1
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    2. Introduction to Part I

      • Luigi Ambrosio, Norman Dancer, Giuseppe Buttazzo, Antonio Marino, M. K. V. Murthy
      Pages 3-4

    3. Geometric evolution problems, distance function and viscosity solutions

      • L. Ambrosio
      Pages 5-93

    4. Variational models for phase transitions, an approach via Γ-convergence

      • G. Alberti
      Pages 95-114

    5. Some aspects of De Giorgi’s barriers for geometric evolutions

      • G. Bellettini, M. Novaga
      Pages 115-151

    6. Partial Regularity for Minimizers of Free Discontinuity Problems with p-th Growth

      • A. Leaci
      Pages 153-169

    7. Free discontinuity problems and their non-local approximation

      • A. Braides
      Pages 171-180

  3. Degree Theory on Convex Sets and Applications to Bifurcation

    1. Front Matter

      Pages 181-181
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    2. Introduction to Part II

      • Luigi Ambrosio, Norman Dancer, Giuseppe Buttazzo, Antonio Marino, M. K. V. Murthy
      Pages 183-184

    3. Degree theory on convex sets and applications to bifurcation

      • E. N. Dancer
      Pages 185-225

    4. Nonlinear elliptic equations involving critical Sobolev exponents

      • D. Passaseo
      Pages 227-241

    5. On the existence and multiplicity of positive solutions for semilinear mixed and Neumann elliptic problems

      • G. Cerami
      Pages 243-258

    6. Solitons and Relativistic Dynamics

      • V. Benci, D. Fortunato
      Pages 259-283

    7. An algebraic approach to nonstandard analysis

      • V. Benci
      Pages 285-326

  4. Back Matter

    Pages 327-347
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Keywords

About this book

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.

Authors, Editors and Affiliations

  • Dipartimento di Matematica, Università di Pisa, Pisa, Italy

    Giuseppe Buttazzo, Antonio Marino, M. K. V. Murthy

  • Scuola Normale Superiore, Pisa, Italy

    Luigi Ambrosio

  • School of Mathematics, University of Sydney, Sydney, Australia

    Norman Dancer

Bibliographic Information

  • Book Title: Calculus of Variations and Partial Differential Equations

  • Book Subtitle: Topics on Geometrical Evolution Problems and Degree Theory

  • Authors: Luigi Ambrosio, Norman Dancer

  • Editors: Giuseppe Buttazzo, Antonio Marino, M. K. V. Murthy

  • DOI: https://doi.org/10.1007/978-3-642-57186-2

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2000

  • Softcover ISBN: 978-3-540-64803-1Published: 24 January 2000

  • eBook ISBN: 978-3-642-57186-2Published: 06 December 2012

  • Edition Number: 1

  • Number of Pages: X, 348

  • Number of Illustrations: 4 b/w illustrations

  • Topics: Calculus of Variations and Optimal Control; Optimization, Systems Theory, Control

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