Seminario / Ciraolo
Il giorno 12 febbraio alle ore 14.30
presso la Sala di Rappresentanza del Dipartimento
il Professor Giulio Ciraolo
(Dipartimento di Matematica dell'Università degli Studi di Milano)
terrà il seguente seminario
Symmetry and stability theorems for problems in geometric analysis and PDEs.
Abstract: We review a series of symmetry and stability results for problems in geometric analysis, for functional inequalities and for overdetermined problems for PDEs, together with some possible applications and open problems.
In particular, we will consider problems related to Alexandrov Soap Bubble Theorem, the Yamabe problem and the prescribe scalar curvature equation, critical points of Sobolev inequality and overdetermined problems for PDEs of Serrin’s type.
The general structure of our result is the following. We first prove that a solution exists if and only if the solution satisfies some symmetry (typically radial symmetry). Once we obtain the symmetry result, it is of interest to investigate its stability counterpart from a quantitative point of view, i.e. we assume that the condition forcing the symmetry is almost satisfied and try to describe what happens to the solution in a quantitative way.
The stability investigation of these problems is very rich, since it may happen that the solution is close to the symmetry configuration as well as a bubbling phenomenon may occur.
Tutti gli interessati sono invitati a partecipare.