Heat kernel estimates for the Dirichlet fractional Laplacian
Zhen-Qing Chen, Panki Kim, Renming Song (2010)
Journal of the European Mathematical Society
Similarity:
We consider the fractional Laplacian on an open subset in with zero exterior condition. We establish sharp two-sided estimates for the heat kernel of such a Dirichlet fractional Laplacian in open sets. This heat kernel is also the transition density of a rotationally symmetric -stable process killed upon leaving a open set. Our results are the first sharp twosided estimates for the Dirichlet heat kernel of a non-local operator on open sets.