Uniqueness and Non-Degeneracy of Minimizers of the Pekar Functional on a Ball
Spectral Methods in Mathematical Physics
27 March 17:00 - 18:00
Dario Feliciangeli - Institute of Science and Technology Austria (IST Austria)
In this talk, we review some properties of the Pekar functional confined to balls. In particular, some recent results, obtained in collaboration with Robert Seiringer and concerning existence, uniqueness and non-degeneracy of minimizers, are presented. These properties were already known to hold on the full space (thanks to works of Lieb and Lenzmann).
The study of the confined case is motivated by a recent paper by Rupert Frank and Robert Seiringer, in which the validity of the aforementioned results is conjectured and taken as a working assumption.
University of Zurich, UZH