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Global Heat Kernel Estimate for Relativistic Stable Processes in Exterior Open Sets by Chen, Zhen-Qing; Kim, Panki; Song, Renming is a scholarly article available to read on EtoBox.

What is Global Heat Kernel Estimate for Relativistic Stable Processes in Exterior Open Sets about?

In this paper, sharp two-sided estimates for the transition densities of relativistic $\alpha$-stable processes with mass $m\in (0, 1]$ in $C^{1,1}$ exterior open sets are established for all time $t>0$. These transition densities are also the Dirichlet heat kernels of $m-(m^{2/\alpha}-\Delta)^{\alpha/2}$ with $m\in (0, 1]$ in $C^{1,1}$ exterior open sets. The estimates are uniform in $m$ in the sense that the constants are independent of $m\in (0, 1]$. As a corollary of our main result, we establish sharp two-sided Green function estimates for relativistic $\alpha$-stable processes with mass $m\in (0, 1]$ in $C^{1,1}$ exterior open sets.

Author

Chen, Zhen-Qing; Kim, Panki; Song, Renming

Published

2011

Language

EN