Albert-Ludwigs-Universität Freiburg Mathematisches Institut Abteilung für Reine Mathematik Arbeitsgruppe Analysis

Aktuelles

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

Inhalt

Syllabus

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.

Vorkenntnisses

• Required previous knowledge: Lineare Algebra I und II, Analysis I–III.
• Recommended previous knowledge: Funktionsanalysis und partielle Differentialgleichungen.

Studienleistung -- Klausur

There will be an oral exam at the end of the course.

Literatur

All the material you need will be provided through ILIAS. No book is needed.

Sprechstunden