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arXiv · 1303.6626

Dirichlet Heat Kernel Estimates for Subordinate Brownian Motions with Gaussian Components

Zhen-Qing Chen·Panki Kim·Renming Song
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Abstract

In this paper, we derive explicit sharp two-sided estimates for the Dirichlet heat kernels, in C^{1,1} open sets D in R^d, of a large class of subordinate Brownian motions with Gaussian components. When D is bounded, our sharp two-sided Dirichlet heat kernel estimates hold for all t>0. Integrating the heat kernel estimates with respect to the time variable t, we obtain sharp two-sided estimates for the Green functions, in bounded C^{1,1} open sets, of such subordinate Brownian motions with Gaussian components.

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Zhen-Qing Chen, Panki Kim, Renming Song. 2013-03-26. Dirichlet Heat Kernel Estimates for Subordinate Brownian Motions with Gaussian Components. https://arxiv.org/abs/1303.6626

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