Book:Haïm Brezis/Functional Analysis, Sobolev Spaces and Partial Differential Equations

Subject Matter

 * Functional Analysis

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


 * 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 Problem


 * 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. Miscellaneous Complements

Solutions of Some Exercises

Problems

Partial Solutions

Notation

References

Index