Partial Differential Equations

Contents

Nonlinear partial differential equations

1. Elliptic equations

Another old table of contents

1. Introduction
2. Method of characteristics
3. Calculus of variations
4. Fourier-analytic methods (requires Fourier analysis)
5. The wave equation (requires integration on manifolds)
6. Fundamental solutions (requires distribution theory)
7. Poisson's equation (requires integration on manyfolds and harmonic function theory)
8. The heat equation
9. Sobolev spaces (requires some functional analysis)
10. Monotone operators (requires convex analysis)

Old table of Contents

Authors should be aware of the stylistic guidelines.

1. Introduction and first examples

Linear partial differential equations

2. The transport equation
3. Test functions
4. Distributions
5. Fundamental solutions, Green's functions and Green's kernels
6. The heat equation
7. Poisson's equation
8. The Fourier transform
9. The wave equation
10. The Malgrange-Ehrenpreis theorem

Nonlinear partial differential equations

11. The characteristic equations
12. Sobolev spaces
13. Convex analysis
14. Calculus of variations
15. Bochner's Integral
16. Monotone operators

17. Answers to the exercises
18. Appendix I: The uniform boundedness principle for (tempered) distributions