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Index
Cover Page
Title Page
Copyright Page
Contents
Introduction
Dedication
CHAPTER 1. FUNCTIONAL ANALYSIS AND DISTRIBUTIONS
1. Introduction
2. Locally Convex Spaces
3. The Space D
4. Differentiation in D' and Examples
5. Differentiation in D' (R1)
6. The Spaces E, J, E', J' and the Fourier Transform
7. Tensor Products and Convolution
8. Topologies in D' and E'—Duality Theory
9. Regularization
10. Some Functional Analysis
11. Vector-Valued Distributions and Integration
CHAPTER 2. ELLIPTIC THEORY
1. Introduction
2. Unbounded Operators—Sobolev Spaces
3. Forms and Operators
4. Some Linear Elliptic Results Following Lions–Magenes
5. Monotonicity—Hemi- and Demicontinuity
6. Nonlinear Elliptic Theory Following F. Browder
7. Some Remarks on Compactness
8. The Calculus of Variations Following F. Browder
9. Variational Methods and Monotone Operators
CHAPTER 3. EVOLUTION EQUATIONS I
1. Introduction
2. Examples from Physics
3. Survey of Hyperbolic and Parabolic Ideas
4. Vector-Valued Ordinary Differential Equations
5. Evolution Operators and Integral Equations
6. Monotonicity and Integral Equations of Evolution Type
CHAPTER 4. EVOLUTION EQUATIONS II (WEAK PROBLEMS)
1. Introduction
2. Some Functional Analysis—Semigroups
3. Weak Linear Problems—Existence Theory
4. Some Functional Analysis—Schwartz Kernels—Operators with Closed Range
5. Uniqueness and Regularity for Weak Problems with Variable Domains
6. More on Uniqueness and Regularity
CHAPTER 5. EVOLUTION EQUATIONS III (STRONG PROBLEMS)
1. Introduction
2. Abstract Strong Problems
3. Interacting Spectra and Interpolation
4. Evolution Operators Following Kato-Tanabe
5. Nonlinear Evolution Equations
6. Spectral Methods for Higher-Order Equations
CHAPTER 6. GLOBAL ANALYSIS
1. Introduction
2. Manifolds
3. Tensors and Forms
4. Vector Bundles
5. Differential Operators in Vector Bundles
6. Elliptic Operators and Index Theory (Sketch)
Appendix I. Some Topology and Fixed-Point Theory
Appendix II. Banach Algebras, Analytic Functional Calculus, Fractional Powers of Operators, and Interpolation Theory
References
Index
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