PhD Course: Nonlinear PDEs and free boundaries

This course will cover basics in viscosity solutions for nonlinear PDEs (now classics), and also free boundary problems (also basics of regularity theory). I shall also mention a few applications of the latter.

Literature:
Cabre-Caffarelli, Fully Nonlinear Elliptic Equations: bookstore.ams.org/view?ProductCode=COLL/43

For Free boundaries and applications I use some parts of my book: bookstore.ams.org/GSM/136

As well as lecture notes to be distributed.

The course will be assessed with take-home assignments and a presentation.