Some notes of the classes (most of the file were updated on 6.11.2023)
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 - Lesson 07.11.2023 - Some exercises (not all have been made in the class)
Optional material, just for curiosity
D - Continuity equation or equation of conservation of mass
This was made in class, but knowing the proof is not required
G - ''Variational nature'' of Laplace equations: the example due to Hadamard
L - An example of a function that is not C^2 and whose Laplacian is continuous