Part I, Viscosity solutions to nonlinear PDEs.

This part treats modern theory of PDE, with geometric methods.

Literature: L.A. Caffarelli and X. Cabre: Fully Nonlinear Elliptic Equations. You may also find other related books/literature on the web.

Topics: Tangent paraboloids and second order differentiability, Viscosity solutions of elliptic equations; Examples, Alexandroff estimate and maximum principle, Harnack Inequality, Uniqueness of solutions, Concave equations, Dirichlet problem.

Part II, Free boundary problems and Applications

I will mostly follow my book, and notes, that I will share with you. https://bookstore.ams.org/gsm-136

Place: Lectures take place at room 3418, at Math building, Tuesdays 13:15--15:00.

Examination: HW & presentation of a topic.

Lecture Notes:	Download HW	Upload Solutions to HW
Crash-Course in Analysis methods in PDE
Fully Nonlinear Notes 1	HW1	HW1
Fully Nonlinear Notes 2	HW2	HW2
Fully Nonlinear Notes 3	HW3	HW3
Fully Nonlinear Notes 4
Free Boundaries Notes 5 Includes several weeks notes and might be updated.	HW for FB HW1 HW2	Upload for HW1 HW2