Department of Mathematics

Topics in PDE: Viscosity Solutions

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Instructors: Prof. Dr. H. Mete Soner and Albert Altarovici Lectures: Thursday 13-15 HG E 41

First Lecture: Thursday, September 19, 2013


Viscosity solutions have been a tremendously successful notion of weak solutions. The theory of viscosity solutions has found applications in many fields and its ability to provide easy convergence proofs has been its main strength.

We first cover the basic theory of viscosity solutions: existence, uniqueness, and stability properties. Then, we discuss some applications: homogenization, mean curvature flow, optimal control, convergence of monotone schemes.


We will follow mainly the paper by Crandall, Ishii, Lions: The User's Guide (available on this site). Related are the lecture notes of Soner on optimal control (to be posted) and the book by Fleming & Soner on optimal control (available online through the ETH network)

The following are also very closely related:

Examination and ECTS Points

Session examination, oral 20 minutes. 4 ECTS Points.


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