For all students

• A - Introduction
  


• B - Classification of (quasi-)linear second order PDEs
  


• C - Some recalls (divergence theorem)
  


• E - A short introduction to distributions
  


• G - ''Variational nature'' of Laplace equations
  


• H - Holomorphic functions and Fundamental solution of Laplacian
  


• I - Properties of harmonic functions
  


• L - Green functions, Poisson formula, Harnack, Liouville
  


• N - The Dirichlet problem in a bounded domain
  


• P - Some exercises (not all have been made in the class)
  

       For mathematical engineering students only

• A - L^p spaces
  


• B - Sobolev spaces in dimension 1
  


• C - Sobolev spaces in dimension greater than 1
  


• D - Variational formulation of some ellittic problems
  


• E - The method of Galerkin (general idea)
  


• F - Regularity results (elliptic case)
  


• G - Some properties of the solutions (elliptic case)
  


• H - Parabolic equations
  

• D - Continuity equation or equation of conservation of mass
  


• G - ''Variational nature'' of Laplace equations: the example due to Hadamard
  


• L - An example of a function that is not C² and whose Laplacian is continuous