For all students

• A - Introduction
  


• B - Classification of (quasi-)linear second order PDEs     Updated on 17^th October
  


• C - Some recalls (divergence theorem)
  


• E - A short introduction to distributions     Updated on 6^th October     Updated on 9^th October
  


• G - ''Variational nature'' of Laplace equations     Updated on 13^th October
  


• H - The fundamental solution
  


• I - Properties of harmonic functions
  


• L - Green function on the ball and half space, Harnack's inequality, Liouville's theorem     Updated on 30^th October    3^rd November
  


• N - The Dirichlet problem in a general domain     Updated on 10^th November
  


• Examples of regular boundary points - Wiener criterion and a very brief mention to the Dirichlet problem in external domains
  




• Some exercises
  




• The gradient and the Laplacian in polar coordinates
  

       For mathematical engineering students only

• A - L^p spaces     Updated on 8^th October
  


• B - Sobolev space in dimension 1
  


• C - Sobolev space in dimension greater than 1     Updated on 18^th November
  


• D - Variational formulation of some elliptic problems     Updated on 3^rd Dicember
  


• F - Regularity results for solutions of linear elliptic equations
  


• G - Some properties of solutions of linear elliptic equations
  


• H - Linear 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