Le vendredi 1er avril 2011, 15 h 30 – 17 h, Concordia University, Library Building, 1400 de Maisonneuve O., LB 921-4, SGW

Sharp estimates on the heat kernels and Green functions of subordinate Brownian motions in smooth domains
Renming Song, University of Illinois

A subordinate Brownian motion is a Lévy process which can obtained by replacing the time of Brownian motion by an independent increasing Lévy process. The infinitesimal generator of a subordinate Brownian motion is $-\phi(-\Delta)$, where $\phi$ is the Laplace exponent of the subordinator. When $\phi(\lambda)=\lambda^{\alpha/2}$ for some $\alpha\in (0, 2)$, we get the fractional Laplacian $-(-\Delta)^{\alpha/2}$ as a special case. In this talk, I will give a survey of some recent results on sharp two-sided estimates on the Dirichlet heat kernels and Green functions of $-\phi(-\Delta)$ in smooth domains.