## EVENT DETAILS AND ABSTRACT

**Analysis Seminar**
**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.

**Date:** Monday, October 18, 2010

**Time:** 4:10pm

**Where:** Lunt 105

**Contact Person:** Prof. Jared Wunsch

**Contact email:** jwunsch@math.northwestern.edu

**Contact Phone:** 847-491-5580

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