Heat kernel estimates for the Dirichlet fractional Laplacian

Chen, Zhen-Qing, Kim, Panki, and Song, Renming. "Heat kernel estimates for the Dirichlet fractional Laplacian." Journal of the European Mathematical Society 012.5 (2010): 1307-1329. <http://eudml.org/doc/277737>.

@article{Chen2010,
abstract = {We consider the fractional Laplacian $-(-\Delta )^\{\alpha /2\}$ on an open subset in $\mathbb \{R\}^d$ with zero exterior condition. We establish sharp two-sided estimates for the heat kernel of such a Dirichlet fractional Laplacian in $C^\{1,1\}$ open sets. This heat kernel is also the transition density of a rotationally symmetric $\alpha $-stable process killed upon leaving a $C^\{1,1\}$ open set. Our results are the first sharp twosided estimates for the Dirichlet heat kernel of a non-local operator on open sets.},
author = {Chen, Zhen-Qing, Kim, Panki, Song, Renming},
journal = {Journal of the European Mathematical Society},
keywords = {fractional Laplacian; symmetric α-stable process; heat kernel; transition density; Green function; exit time; Lévy system; boundary Harnack inequality; parabolic Harnack inequality; intrinsic ultracontractivity; heat kernel; symmetric stable process; exit time; Lévy system; Harnack inequality; intrinsic ultracontractivity},
language = {eng},
number = {5},
pages = {1307-1329},
publisher = {European Mathematical Society Publishing House},
title = {Heat kernel estimates for the Dirichlet fractional Laplacian},
url = {http://eudml.org/doc/277737},
volume = {012},
year = {2010},
}

TY - JOUR
AU - Chen, Zhen-Qing
AU - Kim, Panki
AU - Song, Renming
TI - Heat kernel estimates for the Dirichlet fractional Laplacian
JO - Journal of the European Mathematical Society
PY - 2010
PB - European Mathematical Society Publishing House
VL - 012
IS - 5
SP - 1307
EP - 1329
AB - We consider the fractional Laplacian $-(-\Delta )^{\alpha /2}$ on an open subset in $\mathbb {R}^d$ with zero exterior condition. We establish sharp two-sided estimates for the heat kernel of such a Dirichlet fractional Laplacian in $C^{1,1}$ open sets. This heat kernel is also the transition density of a rotationally symmetric $\alpha $-stable process killed upon leaving a $C^{1,1}$ open set. Our results are the first sharp twosided estimates for the Dirichlet heat kernel of a non-local operator on open sets.
LA - eng
KW - fractional Laplacian; symmetric α-stable process; heat kernel; transition density; Green function; exit time; Lévy system; boundary Harnack inequality; parabolic Harnack inequality; intrinsic ultracontractivity; heat kernel; symmetric stable process; exit time; Lévy system; Harnack inequality; intrinsic ultracontractivity
UR - http://eudml.org/doc/277737
ER -