Functional analysis, Sobolev spaces and partial differential equations
Uniquely, this book presents a coherent, concise and unified way of combining elements from two distinct worlds, functional analysis (FA) and partial differential equations (PDEs), and is intended for students who have a good background in real analysis. This text presents a smooth transition from F...
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| Auteur principal: | |
|---|---|
| Format: | Livre numérique |
| Langue: | Anglais |
| Publié: |
New York, NY :
Springer New York : Springer e-books
[20..].
Cham : Springer Nature |
| Collection: | Universitext
|
| Sujets: | |
| Accès en ligne: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Note: |
Description d'après consultation du 30 janvier 2012 Edition anglaise révisée, mise à jour et étendue avec de nouveaux problèmes et exercices (avec solutions) de l'ouvrage publié en français chez Masson sous le titre : "Analyse fonctionnelle : théorie et applications" (1983) Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Functional analysis, Sobolev spaces and partial differential equations, Haim Brezis, 2011, New York, Springer, 1 vol. (XIII-599 p.), Universitext, 978-0-387-70913-0 |
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| 100 | 1 | |a Brézis, Haïm, |d 1944-2024. | |
| 245 | 1 | 0 | |a Functional analysis, Sobolev spaces and partial differential equations |c Haim Brezis. |
| 260 | |a New York, NY : |b Springer New York : |b Springer e-books. | ||
| 260 | |a Cham : |b Springer Nature, |c [20..]. | ||
| 490 | 1 | |a Universitext | |
| 500 | |a Description d'après consultation du 30 janvier 2012 | ||
| 500 | |a Edition anglaise révisée, mise à jour et étendue avec de nouveaux problèmes et exercices (avec solutions) de l'ouvrage publié en français chez Masson sous le titre : "Analyse fonctionnelle : théorie et applications" (1983) | ||
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 504 | |a Bibliogr. p. 585-594. Index | ||
| 505 | 1 | |a Preface 1. The Hahn Banach Theorems. Introduction to the Theory of Conjugate Convex Functions 2. The Uniform Boundedness Principle and the Closed Graph Theorem. Unbounded Operators. Adjoint. Characterization of Surjective Operators 3. Weak Topologies. Reflexive Spaces. Separable Spaces. Uniform Convexity 4. L^p Spaces 5. Hilbert Spaces 6. Compact Operators. Spectral Decomposition of Self-Adjoint Compact Operators 7. The Hille Yosida Theorem 8. Sobolev Spaces and the Variational Formulation of Boundary Value Problems in One Dimension 9. Sobolev Spaces and the Variational Formulation of Elliptic Boundary Value Problems in N Dimensions 10. Evolution Problems: The Heat Equation and the Wave Equation 11. Some Complements Problems Solutions of Some Exercises and Problems Bibliography Index | |
| 506 | |a Accès en ligne pour les établissements français bénéficiaires des licences nationales | ||
| 506 | |a Accès soumis à abonnement pour tout autre établissement | ||
| 506 | |a Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 | ||
| 520 | |a Uniquely, this book presents a coherent, concise and unified way of combining elements from two distinct worlds, functional analysis (FA) and partial differential equations (PDEs), and is intended for students who have a good background in real analysis. This text presents a smooth transition from FA to PDEs by analyzing in great detail the simple case of one-dimensional PDEs (i.e., ODEs), a more manageable approach for the beginner. Although there are many books on functional analysis and many on PDEs, this is the first to cover both of these closely connected topics. Moreover, the wealth of exercises and additional material presented, leads the reader to the frontier of research. This book has its roots in a celebrated course taught by the author for many years and is a completely revised, updated, and expanded English edition of the important Analyse Fonctionnelle (1983). Since the French book was first published, it has been translated into Spanish, Italian, Japanese, Korean, Romanian, Greek and Chinese. The English version is a welcome addition to this list. The first part of the text deals with abstract results in FA and operator theory. The second part is concerned with the study of spaces of functions (of one or more real variables) having specific differentiability properties, e.g., the celebrated Sobolev spaces, which lie at the heart of the modern theory of PDEs. The Sobolev spaces occur in a wide range of questions, both in pure and applied mathematics, appearing in linear and nonlinear PDEs which arise, for example, in differential geometry, harmonic analysis, engineering, mechanics, physics etc. and belong in the toolbox of any graduate student studying analysis | ||
| 650 | |a Analyse fonctionnelle | ||
| 650 | |a Sobolev, Espaces de | ||
| 650 | |a Équations aux dérivées partielles | ||
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