Contents

Chapters in this book

1. Frontmatter i
2. Preface vii
3. Notation ix
4. Contents xi
5. Part I. Classical Theory
6. Chapter 1. Preliminaries 3
7. Chapter 2. Partial Differential Equations and Mathematical Modeling 13
8. Chapter 3. Elliptic Boundary Value Problems 21
9. Chapter 4. Mixed Problems for Evolution Equations 87
10. Chapter 5. The Cauchy Problem for Evolution Equations 109
11. Part II. Modern Theory
12. Chapter 6. Distributions 131
13. Chapter 7. Sobolev Spaces 149
14. Chapter 8. The Variational Theory of Elliptic Boundary Value Problems 180
15. Part III. Semilinear Equations
16. Chapter 9. Semilinear Elliptic Problems 207
17. Chapter 10. The Semilinear Heat Equation 227
18. Chapter 11. The Semilinear Wave Equation 248
19. Chapter 12 Semilinear Schrödinger Equations 262
20. Bibliography 275
21. Index 278