Dirichlet heat kernel estimates of subordinate diffusions with continuous components in $C^{1, α}$ open sets

Jie-Ming Wang

Published 2024-03-11Version 1

In this paper, we derive explicit sharp two-sided estimates for the Dirichlet heat kernels for a class of subordinate diffusions with continuous components when the scaling order of purely discontinuous part of the subordinator is between $0$ and $1$ including $1$ in $C^{1, \alpha}(\alpha\in (0, 1])$ open sets. As a corollary, we obtain the sharp two-sided estimates for Green functions of these processes in bounded $C^{1, \alpha}$ open sets.