Partial Differential Equations and Functional Analysis

1. Front Matter

   Pages i-xxii

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2. Problèmes aux limites dans des domaines avec points de rebroussement

   • P. Grisvard

   Pages 1-17

3. Elliptic Problems in Domains with Edges: Anisotropic Regularity and Anisotropic Finite Element Meshes

   • Thomas Apel, Serge Nicaise

   Pages 18-34

4. Unique Continuation of Harmonic Functions at Boundary Points and Applications to Problems in Complex Analysis

   • M. S. Baouendi, Linda Preiss Rothschild

   Pages 35-40

5. The Wave Shaping Problem

   • Claude Bardos, Mikhael Belyshev

   Pages 41-59

6. Modélisation mathématique des coques linéairement élastiques

   • Philippe G. Ciarlet

   Pages 60-79

7. Fully Nonlinear Equations by Linearization and Maximal Regularity, and Applications

   • Giuseppe Da Prato

   Pages 80-92

8. Strongly Elliptic Problems Near Cuspidal Points and Edges

   • Monique Dauge

   Pages 93-110

9. Star produit associé à un crochet de Poisson de rang constant

   • Louis Boutet de Monvel

   Pages 111-119

10. La méthode des lâchés de tourbillons pour le calcul des efforts aérodynamiques

    • Philippe Destuynder, Françoise Santi

    Pages 120-131

11. Sum of Operators’ Method in Abstract Equations

    • Angelo Favini

    Pages 132-146

12. Constructive Methods for Abstract Differential Equations and Applications

    • Giuseppe Geymonat, Ouro Tcha-Kondor

    Pages 147-159

13. On Asymptotics of Solutions of Nonlinear Second Order Elliptic Equations in Cylindrical Domains

    • V. A. Kondratiev, O. A. Oleinik

    Pages 160-173

14. Singularities in Solutions to Mathematical Physics Problems in Non-Smooth Domains

    • V. A. Kozlov, V. G. Maz’ya

    Pages 174-206

15. Problèmes sensitifs et coques élastiques minces

    • J.-L. Lions, E. Sanchez-Palencia

    Pages 207-220

16. Contrôlabilite exacte frontière de l’équation des ondes en presence de singularités

    • Mary Teuw Niane

    Pages 221-234

17. Interpolation and Extrapolation Spaces in Evolution Equations

    • E. Sinestrari

    Pages 235-254

18. Localisation des singularités sur la frontière et partitions de l’unité

    • Martin Zerner

    Pages 255-263

19. Back Matter

    Pages 265-266

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Pierre Grisvard, one of the most distinguished French mathematicians, died on April 22, 1994. A Conference was held in November 1994 out of which grew the invited articles contained in this volume. All of the papers are related to functional analysis applied to partial differential equations, which was Grisvard's specialty. Indeed his knowledge of this area was extremely broad. He began his career as one of the very first students of Jacques Louis Lions, and in 1965, he presented his "State Thesis" on interpolation spaces, using in particular, spectral theory for linear operators in Banach spaces. After 1970, he became a specialist in the study of optimal regularity for par­ tial differential equations with boundary conditions. He studied singulari­ ties coming from coefficients, boundary conditions, and mainly non-smooth domains, and left a legacy of precise results which have been published in journals and books. Pierre Grisvard spent most of his career as a full professor at the University of Nice, where he started in 1967. For shorter or longer periods, he visited several foreign countries, and collaborated with some of the most famous mathematicians in his field. He was also an excellent organizer and directed a large number of Ph.D. students. Finally, this volume contains a bibliography of Grisvard's works as well as one paper which he wrote and which has not been published before.

• Finite
• Mathematica
• banach spaces
• calculus
• complex analysis
• differential equation
• equation
• function
• functional analysis
• interpolation
• mathematical physics
• maximum
• partial differential equation
• spectral theory
• partial differential equations

• Laboratoire de Mathématiques, University of Nice, Nice Cedex, France

  Jean Cea, Denise Chenais

• Laboratoire de Mathématiques, Ecole Normale Supérieure, Cachan Cedex, France

  Giuseppe Geymonat

• Collège de France, Paris, France

  Jacques Louis Lions

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