Fractional Sobolev Spaces and Boundary Value Problems
What is this about? In the analysis of partial differential equations, in particular of diffusion type, Sobolev spaces are essential in giving a suitable framework for the study of such. One of the Sobolev spaces that sticks out is the one associated to a weak formulation of problems involving the Laplacian. This space consists of those functions being of order one differentiable with an L²-integrability. In this course we give a natural extension of the meaning "order-one-differentiability" to any nonnegative order of differentiability. This leads to the so-called "fractional Sobolev spaces". Within this course, we will also give an understanding of what "natural extension" means and we will study in particular the operators which are associated to these fractional Sobolev spaces. Similarly, as the Laplacian is an operator of order two -- 2=2 times the order of the associated Sobolev space -- the operators associated to fractional Sobolev spaces are of "fractional order" and the associated boundary value problems can hence be seen as "fractional boundary value problems".
Lecture time and other information:
This lecture will be held next in the summer term 2020. The lecture times are from April 20th to June 12th please note that the lecture will be held in English and it is part of the moduls MaM-FFA-k (advanced functional analysis) or MaM-FPD-k (advanced partial differential equations). Due to being a "small" course, the lecture hence ends after June 5th. In addition to the lecture, there is a weekly excercise course (until June 5th).
Further informations on the course, as the excercise sheets and the lecture notes can be found on OLAT.