Partial Differential Equations

Contents

edit

Linear partial differential equations

edit

Nonlinear partial differential equations

edit
  1. Elliptic equations

Another old table of contents

edit
  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

edit

Authors should be aware of the stylistic guidelines.

 
  1. Introduction and first examples  

Linear partial differential equations

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

Nonlinear partial differential equations

edit
  1. The characteristic equations  
  2. Sobolev spaces  
  3. Convex analysis  
  4. Calculus of variations  
  5. Bochner's Integral  
  6. Monotone operators  


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