Partial Differential Equations and the Calculus of Variations

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

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.

• Calculus of Variations
• Optimal control
• calculus
• differential equation
• mathematical analysis
• maximum
• minimum
• ordinary differential equation
• partial differential equation
• partial differential equations

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

  Ferruccio Colombini, Antonio Marino, Luciano Modica, Sergio Spagnolo

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