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...
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| Format: | eBook |
| Language: | English |
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New York, NY
Springer New York
2011, 2011
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| Edition: | 1st ed. 2011 |
| Series: | Universitext
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| Subjects: | |
| Online Access: | |
| Collection: | Springer eBooks 2005- - Collection details see MPG.ReNa |
Table of Contents:
- 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