Around the Nash-Moser theorem

These are lecture notes corresponding to a master course taught in University Paris Diderot in 2019. Download here.

Table of contents :

1. Iterative methods for solving nonlinear equations
2. Conjugacy of circle diffeomorphisms
3. The Nash-Moser theorem
4. The isometric embedding of Riemannian Manifolds
5. Littlewood-Paley decomposition
6. The regularity theorem of De Giorgi for scalar elliptic equations