EVENT DETAILS AND ABSTRACT

Title: Sharp two-sided estimates on the heat kernels and Green functions of subordinate Brownian motions in smooth domains
Speaker: Renming Song
Speaker Info: University of Illinois, Urbana-Champaign
Brief Description:
Special Note:
Abstract:

A subordinate Brownian motion is a L\'evy process which can obtained by replacing the time of Brownian motion by an independent increasing Levy 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.