Functional Analysis, Sobolev Spaces and Partial Differential Equations
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.