For all students

• A - Introduction
  


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


• C - Some recalls (divergence theorem)
  


• D - Definizione di spazio di Sobolev e qualche esempio di funzione di Sobolev in dimensione 1
  


• D - Definizione di spazio di Sobolev e qualche esempio di funzione di Sobolev in dimensione maggiore di 1
  


• E - A short introduction to distributions
  


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


• H - The fundamental solution
  


• I - Properties of harmonic functions
  


• L - Green function on the ball and half space, Harnack's inequality, Liouville's theorem
  


• N - The Dirichlet problem in a general domain
  


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




• Alcuni altri esercizi proposti
  



• The gradient and the Laplacian in polar coordinates
  

• 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