After successful completion of the course, students are able to give proof for the existence of weak solutions of different classes of nonlinear elliptic and parabolic differential equations; they are able to use maximum principles for weak solutions; furthermore the students learn how to use the theory of viscous solutions for Hamilton-Jacobi-equations and to present solutions to a group of other students.

- semilinear elliptic equations

- quasilinear elliptic equations

- semilinear parabolic equations

- quasilinear parabolic equations

- stationary Navier-Stokes equations

- Schroedinger equations

- Hamilton-Jacobi equations

Lectures and an accompanying exercise are being offered. In the lecture, the theory is introduced and examples are calculated. In addition, a script is offered to deepen the lecture material.
In the accompanying exercise, weekly exercise sheets are handed out, which are calculated by the students in the exercise on the blackboard.

The course will be held in person apart from a few exceptions. The announcement of the specific exceptions (online) and the further communication for the lecture takes place through the assigned TUWEL course.

Lecture notes (German) are available on the webpage: https://www.asc.tuwien.ac.at/juengel/scripts/nPDE.pdf
The English version is available in the assigned TUWEL course.

The first lecture will be held on: Tuesday, 05.03.2024, 13.30-15.00.

Exercises and presentation on the blackboard for UE; oral exam for VO

In case that the oral exam is offered(needs to be offered online: Two devices with camera (e.g. laptop or tablet and smartphone) are needed.

Lecture notes for this course are available; online auf der Homepage des Vortragenden

https://www.asc.tuwien.ac.at/juengel/scripts/nPDE.pdf

Further teaching material can be found at Tuwel.

Linear partial differential equations; functional analysis