| Bemerkung |
The study of certain PDEs may be particularly challenging due to the presence of high degenerate structure associated to these types of equations. Some examples of these PDEs may be, for instance, the equations with the fractional Laplacian operator or the eikonal equation. These PDEs are interesting to be studied not only in a theoretical framework but also for applications (e.g. crystallography).
In this course fractional Sobolev spaces and viscosity solutions will be introduced and studied in order to understand how to approach these equations. At the end of the course there will be a digression related to the mean curvature flow, which is a geometric evolution with a direct impact in recostruction of images and neurogeometry. This will be a practical example of why these generalised solutions are well defined and more useful to study these types of problem rather than the standard ones." |
