Seminari del Dipartimento di Matematica

Seminario del 2013

Dr. Wei-Xi Li, Dipartimento di Matematica, Universita` di Bologna

Global hypoellipticity and symbolic estimates for the linearized Boltzmann operator without angular cutoff

analisi matematica

In this talk we provide global subelliptic estimates for the linearized inhomogeneous Boltzmann equation without angular cutoﬀ, and show that some global gain in the spatial direction is available although the corresponding operator is not elliptic in this direction. The proof is based on a multiplier method and the so-called Wick quantization, together with a careful analysis of the symbolic properties of the Weyl symbol of the Boltzmann collision operator. This is a joint work with R. Alexandre and F.Herau.