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Functional Analysis, Sobolev Spaces and Partial Differential Equations

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Buch | Softcover
600 Seiten
2010
Springer-Verlag New York Inc.
978-0-387-70913-0 (ISBN)

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Functional Analysis, Sobolev Spaces and Partial Differential Equations - Haim Brezis
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This textbook is a completely revised, updated, and expanded English edition of the important Analyse fonctionnelle (1983). Uniquely, this book presents in a coherent, concise and unified way the main results from functional analysis together with the main results from the theory of partial differential equations (PDEs).
This textbook is a completely revised, updated, and expanded English edition of the important Analyse fonctionnelle (1983). In addition, it contains a wealth of problems and exercises (with solutions) to guide the reader. Uniquely, this book presents in a coherent, concise and unified way the main results from functional analysis together with the main results from the theory of partial differential equations (PDEs). Although there are many books on functional analysis and many on PDEs, this is the first to cover both of these closely connected topics. Since the French book was first published, it has been translated into Spanish, Italian, Japanese, Korean, Romanian, Greek and Chinese. The English edition makes a welcome addition to this list.

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.

Erscheint lt. Verlag 10.11.2010
Reihe/Serie Universitext
Zusatzinfo XIV, 600 p.
Verlagsort New York, NY
Sprache englisch
Maße 155 x 235 mm
Themenwelt Mathematik / Informatik Mathematik Analysis
ISBN-10 0-387-70913-4 / 0387709134
ISBN-13 978-0-387-70913-0 / 9780387709130
Zustand Neuware
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