Non Local Elliptic Equations, Sommersemester 2020
|| Donnerstags, 12-14 Uhr
|| SR 403, Ernst-Zermelo-Straße 1
Due to the current circumstances, the lecture will be carried out digitally. Please register on the online system HISinOne.
- The material will be provided through ILIAS
- The lecture will take place online in the BBB room
| Fischer |
This course covers the basic knowledge of non-local elliptic equations.
- First, we will provide an overview of local elliptic PDEs and Browian motions which will lead to the introduction of non-local elliptic PDEs.
- Then, we will cover the main known results for the model non-local operator: the fractional Laplacian. This will include definition, existence of solutions, fundamental solution, mean value properties, extension problem and regularity.
- Next, we will study linear integro-differential equarions: Lévy processes, weak solutions and regularity.
- Finally, we will give some ideas about what happens for the case of non-linear equations and we will also provide some results for more general kernels.
The presentation will be at a basic level and technicalities will be kept to a minimum.
The course language is English.
- Required previous knowledge: Lineare Algebra I und II, Analysis I–III.
- Recommended previous knowledge: Funktionsanalysis und partielle Differentialgleichungen.
There will be an oral exam at the end of the course.
All the material you need will be provided through ILIAS. No book is needed.
|Dr. Azahara DelaTorre Pedraza
| Di 11:30-12:30 Uhr (Studenten), Di 14:00-16:00 Uhr (Tutoren)
Ernst-Zermelo-Straße 1, Raum 214