8 sep 2021 -- 09:30   [open in google calendar]

Abstract.

We consider the constrained critical values of the Dirichlet integral on the unit $L^q$ sphere. This leads to a semilinear eigenvalue type equation. We focus on some properties of the relevant spectrum and connections with the Lane-Emden equation. We also present some applications to the large behaviour of solutions to nonlinear diffusion equations of porous medium type.

The talk is based on collaborations with Guido De Philippis (Courant Institute), Giovanni Franzina (CNR) and Bruno Volzone (Napoli Parthenope).