240163 Nonlocal Operators (PDE 3) (V) (SoSe 2026)

The focus of this course is on non-local operators of fractional order. We concentrate on operators with a differentiability order between zero and two, which are therefore also referred to as integro-differential operators. This lecture can be taken independently of the courses PDE 1 and PDE 2, as the necessary concepts will be introduced as needed. However, a solid understanding of those courses is advantageous, as we will work extensively with analogies to the familiar world of differential operators. Ideally, we will succeed in developing a theory analogous to that of De Giorgi-Moser-Nash for second-order differential operators.

The non-local operators under consideration have many applications in current research, such as in the study of Markov jump processes or image processing. I am very happy to accommodate the specific requests and interests of students.

Teilnahmevoraussetzungen, notwendige Vorkenntnisse

Knowledge of Analysis, Functional Analysis and ideally some theory of partial differential equations.

Literaturangaben

Will be added shortly.