Unique continuation properties for nonlocal operators
María Ángeles García-Ferrero (University of Heidelberg)
Abstract: Roughly speaking, a unique continuation property states that a solution of certain partial differential equation is determined by its behaviour in a subset. In this talk we will see this kind of properties, including their strong and quantitative versions, for some classes of nonlocal operators like the Hilbert transform, which arise in medical imaging, or the (higher order) fractional Laplacian. The results I will present rely on commonly used tools as Carleman estimates and the Caffareli-Silvestre extension, but also on two alternative mechanisms. As an application we will see Runge approximation results.
This is joint work with Angkana Rüland.
analysis of PDEsclassical analysis and ODEs
Audience: researchers in the topic
Series comments: Description: A senior graduate student/postdoc series in harmonic analysis, geometric measure theory, and partial differential equations.
Meetings will be weekly, and usually will occur on Monday, with some exceptions. For each talk, the Zoom link is made available in the website too. Contact Bruno Poggi at poggi008@umn.edu if you would like to subscribe to the seminar mailing list.
| Organizers: | Bruno Poggi*, Ryan Matzke, Jose Luis Luna Garcia* |
| *contact for this listing |