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Calculus of Variations and Nonlinear Partial Differential Equations

Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, June 27 - July 2, 2005

  • Book
  • © 2008

Overview

Authors:
  1. Luigi Ambrosio

    1. Scuola Normale Superiore, Italy

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  2. Luis Caffarelli

    1. Department of Mathematics, University of Texas at Austin, Austin, USA

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  3. Michael G. Crandall

    1. Department of Mathematics, University of California, Santa Barbara, USA

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  4. Lawrence C. Evans

    1. Department of Mathematics, University of California, Berkeley, USA

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  5. Nicola Fusco

    1. Dipartimento di Matematica, Università degli Studi di Napoli, Via Cintia, Italy

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Editors:
  1. Bernard Dacorogna

    1. Section de Mathématiques, Ecole Polytechnique Fédérale de Lausanne (EPFL), Switzerland

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  2. Paolo Marcellini

    1. Dipartimento di Matematica, Università di Firenze, Italy

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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1927)

Part of the book sub series: C.I.M.E. Foundation Subseries (LNMCIME)

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Table of contents (6 chapters)

  1. Front Matter

    Pages I-XI
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  2. Transport Equation and Cauchy Problem for Non-Smooth Vector Fields

    • Luigi Ambrosio
    Pages 1-41

  3. Issues in Homogenization for Problems with Non Divergence Structure

    • Luis Caffarelli, Luis Silvestre
    Pages 43-74

  4. A Visit with the ∞-Laplace Equation

    • Michael G. Crandall
    Pages 75-122

  5. Weak KAM Theory and Partial Differential Equations

    • Lawrence C. Evans
    Pages 123-154

  6. Geometrical Aspects of Symmetrization

    • Nicola Fusco
    Pages 155-181

  7. CIME Courses on Partial Differential Equations and Calculus of Variations

    • Elvira Mascolo
    Pages 183-189

  8. Back Matter

    Pages 193-204
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Keywords

About this book

This volume provides the texts of lectures given by L. Ambrosio, L. Caffarelli, M. Crandall, L.C. Evans, N. Fusco at the Summer course held in Cetraro (Italy) in 2005. These are introductory reports on current research by world leaders in the fields of calculus of variations and partial differential equations. The topics discussed are transport equations for nonsmooth vector fields, homogenization, viscosity methods for the infinite Laplacian, weak KAM theory and geometrical aspects of symmetrization. A historical overview of all CIME courses on the calculus of variations and partial differential equations is contributed by Elvira Mascolo.

Authors, Editors and Affiliations

  • Section de Mathématiques, Ecole Polytechnique Fédérale de Lausanne (EPFL), Switzerland

    Bernard Dacorogna

  • Dipartimento di Matematica, Università di Firenze, Italy

    Paolo Marcellini

  • Scuola Normale Superiore, Italy

    Luigi Ambrosio

  • Department of Mathematics, University of Texas at Austin, Austin, USA

    Luis Caffarelli

  • Department of Mathematics, University of California, Santa Barbara, USA

    Michael G. Crandall

  • Department of Mathematics, University of California, Berkeley, USA

    Lawrence C. Evans

  • Dipartimento di Matematica, Università degli Studi di Napoli, Via Cintia, Italy

    Nicola Fusco

Bibliographic Information

  • Book Title: Calculus of Variations and Nonlinear Partial Differential Equations

  • Book Subtitle: Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, June 27 - July 2, 2005

  • Authors: Luigi Ambrosio, Luis Caffarelli, Michael G. Crandall, Lawrence C. Evans, Nicola Fusco

  • Editors: Bernard Dacorogna, Paolo Marcellini

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/978-3-540-75914-0

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2008

  • Softcover ISBN: 978-3-540-75913-3Published: 03 December 2007

  • eBook ISBN: 978-3-540-75914-0Published: 10 December 2007

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: XI, 206

  • Topics: Calculus of Variations and Optimal Control; Optimization, Partial Differential Equations

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