| Abstract: |
| We consider some n-dimensional functional inequalities of the type of Poincar\`e, with weight, for isotropic probability densities. Unlike previous studies, for example by S.G. Bobkov, and M. Ledoux (Ann. Probab. 37 (2009)), the derivation of these inequalities is strongly related to their connection with the problem of convergence to equilibrium for a class of Fokker--Planck type equations characterized by a variable coefficient of diffusion. This is a result obtained in collaboration with G. Furioli (Univ. of Bergamo, Italy), A. Pulvirenti and G. Toscani (Univ. of Pavia, Italy). |
|