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Partial Differential Equations and the Calculus of Variations

Essays in Honor of Ennio De Giorgi Volume 1

  • Book
  • © 1989

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Editors:
  1. Ferruccio Colombini

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

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  2. Antonio Marino

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

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  3. Luciano Modica

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

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  4. Sergio Spagnolo

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

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Part of the book series: Progress in Nonlinear Differential Equations and Their Applications (PNLDE, volume 1)

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Table of contents (21 chapters)

  1. Front Matter

    Pages i-xxii
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  2. An Improvement of Cartan’s Test for Ordinarity

    • William K. Allard
    Pages 1-8

  3. A Mathematical Contribution to Gibbs’s Analysis of Fluid Phases in Equilibrium

    • Frederick J. Almgren, Morton E. Gurtin
    Pages 9-28

  4. The Epi-Continuation Method for Minimization Problems. Relation with the Degree Theory of F. Browder for Maximal Monotone Operators

    • Hedy Attouch, Hassan Riahi
    Pages 29-58

  5. Discretization of Evolution Variational Inequalities

    • Claudio Baiocchi
    Pages 59-92

  6. Homogenization for Non Linear Elliptic Equations with Random Highly Oscillatory Coefficients

    • Alain Bensoussan
    Pages 93-133

  7. L ∞ and L 1 Variations on a Theme of Γ-Convergence

    • Lucio Boccardo
    Pages 135-147

  8. Asymptotics for Elliptic Equations Involving Critical Growth

    • Haïm Brezis, Lambertus A. Peletier
    Pages 149-192

  9. Asymptotic Behaviour for Dirichlet Problems in Domains Bounded by Thin Layers

    • Giuseppe Buttazzo, Gianni Dal Maso, Umberto Mosco
    Pages 193-249

  10. Fundamental Interior Estimates for a Class of Second Order Elliptic Operators

    • Sergio Campanato
    Pages 251-259

  11. Γ-Convergence of Integral Functionals Defined on Vector-Valued Functions

    • Luciano Carbone, Riccardo De Arcangelis
    Pages 261-283

  12. Limits of Obstacle Problems for the Area Functional

    • Michele Carriero, Gianni Dal Maso, Antonio Leaci, Eduardo Pascali
    Pages 285-309

  13. Some Remarks on the Well-Posedness of the Cauchy Problem in Gevrey Spaces

    • Lamberto Cattabriga
    Pages 311-319

  14. Approximating Measures and Rectifiable Curves

    • Antonio Chiffi
    Pages 321-329

  15. A Non-Uniqueness Result for the Operators with Principal Part \( partial _t^2 {\text{ }} + {\text{ a}}\left( t \right)\partial _x^2 \)

    • Ferruccio Colombini, Sergio Spagnolo
    Pages 331-353

  16. A Note on Duality and the Calculus of Variations

    • Ubiratan D’Ambrosio
    Pages 355-358

  17. Some Results on Periodic Solutions of Hamilton-Jacobi Equations in Hilbert Spaces

    • Giuseppe Da Prato
    Pages 359-370

  18. Generalized Solutions to Ordinary Differential Equations with Discontinuous Right-Hand Sides Via Γ-Convergence

    • Zofia Denkowska, Zdzislaw Denkowski
    Pages 371-400

  19. Stationary Solutions of Nonlinear Schrödinger Equations with an External Magnetic Field

    • Maria J. Esteban, Pierre-Louis Lions
    Pages 401-449

  20. On the Touching Principle

    • Robert Finn, Enrico Giusti
    Pages 451-460
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Keywords

About this book

The Italian school of Mathematical Analysis has long and glo­ rious traditions. In the last thirty years it owes very much to the scientific pre-eminence of Ennio De Giorgi, Professor of Mathemati­ cal Analysis at the Scuola Normale Superiore di Pisa. His fundamental theorems in Calculus of Variations, in Minimal Surfaces Theory, in Partial Differential Equations, in Axiomatic Set Theory as well as the fertility of his mind to discover both general mathematical structures and techniques which frame many different problems, and profound and meaningful examples which show the limits of a theory and give origin to new results and theories, makes him an absolute reference point for all Italian mathematicians, and a well-known and valued personage in the international mathematical world. We have been students of Ennio de Giorgi. Now, we are glad to present to him, together with all his collegues, friends and former students, these Essays of Mathematical Analysis written in his hon­ our on the occasion of his sixtieth birthday (February 8th, 1988), with our best wishes and our thanks for all he gave in the past and will give us in the future. We have added to the research papers of this book the text of a conversation with Ennio De Giorgi about the diffusion and the communication of science and, in particular, of Mathematics.

Editors and Affiliations

  • Dipartimento di Matematica, Universita di Pisa, Pisa, Italy

    Ferruccio Colombini, Antonio Marino, Luciano Modica, Sergio Spagnolo

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