Partial Differential Equations

ContentsEdit

Linear partial differential equationsEdit

Nonlinear partial differential equationsEdit

  1. Elliptic equations

Another old table of contentsEdit

  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 ContentsEdit

Authors should be aware of the stylistic guidelines.

  1. Introduction and first examples  

Linear partial differential equationsEdit

  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 equationsEdit

  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