Zhen-Qing Chen University of Washington, Seattle
Title: Dirichlet Heat Kernel Estimates for Fractional Laplacians Perturbed by Gradient Operators
Associated with the non-local operator $L$ on Euclidean space that is a fractional Laplacian perturbed by a gradient operator is a strong Markov process $X$ which is a rotationally symmetric stable process with a drift. Let $D$ be a bounded open set. In this talk, I will present recent results of sharp two-sided estimates on the the fundamental solution (or heat kernel) of the non-local operator $L$ on $D$ with zero exterior condition. This fundamental solution is also the transition density p_D (t, x, y) of the sub-process of X killed open leaving the bounded open set D. Based on joint work with P. Kim and R. Song.
©2010, Department of Mathematical Sciences
Last Modified: February 26, 2009