## An inverse function theorem in C^infty

### Ivar Ekeland

created by ambrosio on 14 Mar 2011

22 mar 2011

Abstract.

Ennio De Giorgi Colloquium and seminar

IVAR EKELAND

CEREMADE et Institut de Finance Universitè Paris-Dauphine

Aula Dini, Scuola Normale Superiore

22 Marzo 2011

14.00-15.00. Colloquio De Giorgi 15.00-15.30. Coffee break 15.30.17.00. Seminar

Title: An inverse function theorem in Cinfty

Abstract: We state and prove a "hard" inverse function theorem which extends the classical theorem of Nash and Moser. In contrast with the latter, we do not use the Newton iteration procedure, so we do not require that the function to be inverted is $C^2$, or even $C^1$, or even Frechet-differentiable. The proof is direct, and relies on Ekeland's variational principle. During the colloquium, we will explain the method and prove the theorem in the "easy" case (Banach spaces) and during the afterwards seminar we will provide the proof in the "hard" case (Frechet spaces)