Partial Differential Equations

This three-volume work is published as Vols. 115-117 in the Applied Math. Sciences series of Springer-Verlag. The first volume is also available in paperback, as Vol. 23 of Springer's series, Texts in Applied Math. Below there is a list of chapters for each volume. One can click on each volume for a more detailed table of contents.

Vol. 1: Basic Theory

1. Basic Theory of ODE and Vector Fields
2. The Laplace Equation and Wave Equation
3. Fourier Analysis, Distributions, and Constant-Coefficient Linear PDE
4. Sobolev Spaces
5. Linear Elliptic Equations
6. Linear Evolution Equations
A. Outline of Functional Analysis
B. Manifolds, Vector Bundles, and Lie Groups

Vol. 2: Qualitative Studies of Linear Equations

7. Pseudodifferential Operators
8. Spectral Theory
9. Scattering by Obstacles
10. Dirac Operators and Index Theory
11. Brownian Motion and Potential Theory
12. The Dbar-Neumann Problem
C. Connections and Curvature

Vol. 3: Nonlinear Equations

13. Function Space and Operator Theory for Nonlinear Analysis
14. Nonlinear Elliptic Equations
15. Nonlinear Parabolic Equations
16. Nonlinear Hyperbolic Equations
17. Euler and Navier-Stokes Equations for Incompressible Fluids
18. Einstein's Equations