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Einladung zum Vortrag (Zoom) von Frau Prof. Dr. Hanne Van Den Bosch (University of Chile, Santiago) am 07.12.2022 - 14:30 Uhr im Rahmen des Forschungsseminars Analysis
[07.12.2022]Im Rahmen des Forschungsseminars Analysis hält am Mittwoch, den 7. Dezember 2022, um 14:30 Uhr,
Frau Prof. Dr. Hanne Van Den Bosch (University of Chile, Santiago)
einen Vortrag zum Thema
A Keller-Lieb-Thirring Inequality for Dirac operators
Abstract: The classical Keller-Lieb-Thirring inequality bounds the ground state energy of a Schrödinger operator by a Lebesgue norm of the potential. This problem can be rewritten as a minimization problem for the Rayleigh quotient over both the eigenfunction and the potential. It is then straightforward to see that the best potential is a power of the eigenfunction, and the optimal eigenfunction satisfies a nonlinear Schrödinger equation.
This talk concerns the analogous question for the smallest eigenvalue in the gap of a massive Dirac operator. This eigenvalue is not characterized by a minimization problem. By using a suitable Birman-Schwinger operator, we show that for sufficiently small potentials in Lebesgue spaces, an optimal potential and eigenfunction exists. Moreover, the corresponding eigenfunction solves a nonlinear Dirac equation.
This is joint work with Jean Dolbeault, David Gontier and Fabio Pizzichillo.
Der Vortrag findet im Rahmen eines Zoom-Meetings statt. Bei Interesse an den Zugangsdaten bitte bei Herrn Prof. Mugnolo (delio.mugnolo@fernuni-hagen.de) melden.
