About symmetry and symmetry breaking for extremal functions in interpolation functional inequalities

Math Physics Seminar
Wednesday, January 19, 2011 - 16:30
1 hour (actually 50 minutes)
Skiles 006
CEREMADE, University of Paris, Dauphine
In this talk I will present recent work, in collaboration with J.Dolbeault, G. Tarantello and A. Tertikas,about the symmetry properties of extremal functions for (interpolation)functional inequalities playing an important rolein the study of long time behavior of evolution diffusion equations.Optimal constants are rarely known,in fact one can write them explicitely only when the extremals enjoymaximal symmetry. This is why the knowledge of the parameters' regionswhere symmetry is achieved is of big importance.  In the case of symmetrybreaking, the underlying phenomena permitting it are analyzed.