Introduction to the Nash-Moser implicit function theorem

April 24 - 27, 2023

Online mini-course "Introduction to the Nash-Moser implicit function theorem"

Wuhan University (China)

Lecturer: prof. Paolo Secchi (Brescia)

The aim of the course is to provide an introduction to the Nash-Moser implicit function theorem, as a tool for the resolution of nonlinear differential equations, where the linearized problems admit estimates with a loss of derivatives with respect to the given data.

We first introduce the local inversion theorem and the standard implicit function theorem, and discuss some examples where these theorems are sufficient. Then we briefly introduce the isometric embedding problem, that is the problem originally solved by J. Nash in 1956, using an iteration technique taken up again by J. Moser in 1961, and subsequently known as the Nash-Moser method. We also discuss a simple boundary value problem for the wave equation that may admit estimates with a loss of derivatives from the data. Finally, we present the Nash-Moser implicit function theorem with a simplified scheme of proof.

Schedule (Italy time):

April 24: 9:00-12:00

April 25: 9:00-12:00

April 27: 9:00-12:00

The lectures will be delivered via Zoom:

ZOOM-ID: 820 6413 2631

Password: tmcc202304