This course will follow a series of works about the symmetry properties of extremal functions for (interpolation) functional inequalities playing an important role in the study of long time behavior of evolution diffusion equations.
Optimal constants are rarely known, in fact one can write them explicitly only when the extremals enjoy maximal symmetry. This is why the knowledge of the parameters' regions where symmetry is achieved is of big importance.
This course will present variational methods used to prove existence of extremal functions and then various methods (symetrization, spectral, etc) used to prove or disprove symmetry. Most of the interesting phenomena arising here will be proved analytically, but numerical results will be also presented, because some of them shed a very interesting light on symmetry breaking phenomena which are of a new and surprising nature.
Vortragsreihe im Rahmen des Graduiertenkollegs 1838 „Spektraltheorie und Dynamik von Quantensystemen“
Dienstag, 01. April 2014 und Donnerstag, 03. April 2014
jeweils 11.00-12.30 Uhr sowie 14.30-16.00 Uhr