TY - JOUR
T1 - Heat kernel estimates for dirichlet fractional laplacian with gradient perturbation
AU - Chen, Peng
AU - Song, Renming
AU - Xie, Longjie
AU - Xie, Yingchao
N1 - Publisher Copyright:
© 2019 Korean Mathematical Society.
PY - 2019
Y1 - 2019
N2 - We give a direct proof of the sharp two-sided estimates, recently established in [4,9], for the Dirichlet heat kernel of the fractional Laplacian with gradient perturbation in C 1,1 open sets by using Duhamel's formula. We also obtain a gradient estimate for the Dirichlet heat kernel. Our assumption on the open set is slightly weaker in that we only require D to be C 1,θ for some θ ∈ (α/2,1].
AB - We give a direct proof of the sharp two-sided estimates, recently established in [4,9], for the Dirichlet heat kernel of the fractional Laplacian with gradient perturbation in C 1,1 open sets by using Duhamel's formula. We also obtain a gradient estimate for the Dirichlet heat kernel. Our assumption on the open set is slightly weaker in that we only require D to be C 1,θ for some θ ∈ (α/2,1].
KW - Dirichlet heat kernel
KW - Fractional Laplacian
KW - Gradient estimate
KW - Isotropic stable process
KW - Kato class
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U2 - 10.4134/JKMS.j180065
DO - 10.4134/JKMS.j180065
M3 - Article
AN - SCOPUS:85062662152
SN - 0304-9914
VL - 56
SP - 91
EP - 111
JO - Journal of the Korean Mathematical Society
JF - Journal of the Korean Mathematical Society
IS - 1
ER -