Functional Analysis, Sobolev Spaces and Partial Differential Equations

• Main Author: Brezis, Haim (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: New York, NY : Springer New York, 2011.
• Series: Universitext
• Subjects: Mathematics.; Difference equations.; Functional equations.; Functional analysis.; Partial differential equations.; Functional Analysis.; Partial Differential Equations.; Difference and Functional 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...

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.