Dirichlet heat kernel estimates for fractional laplacian with gradient perturbation

Zhen Qing Chen; Panki Kim; Renming Song

doi:10.1214/11-AOP682

Dirichlet heat kernel estimates for fractional laplacian with gradient perturbation

Zhen Qing Chen^*, Panki Kim, Renming Song

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66 引用（Scopus）

摘要

Suppose that d ≥ 2 and α ∈ (1, 2). Let D be a bounded C^1,1 open set in R^d and b an R^d -valued function on R^d whose components are in a certain Kato class of the rotationally symmetric α-stable process. In this paper, we derive sharp two-sided heat kernel estimates for L^b = δ^α/2 + b. ∇ in D with zero exterior condition. We also obtain the boundary Harnack principle for L^b in D with explicit decay rate.

源语言	英语
页（从-至）	2483-2538
页数	56
期刊	Annals of Probability
卷	40
期	6
DOI	https://doi.org/10.1214/11-AOP682
出版状态	已出版 - 2012
已对外发布	是

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Chen, Z. Q., Kim, P., & Song, R. (2012). Dirichlet heat kernel estimates for fractional laplacian with gradient perturbation. Annals of Probability, 40(6), 2483-2538. https://doi.org/10.1214/11-AOP682

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title = "Dirichlet heat kernel estimates for fractional laplacian with gradient perturbation",

abstract = "Suppose that d ≥ 2 and α ∈ (1, 2). Let D be a bounded C1,1 open set in Rd and b an Rd -valued function on Rd whose components are in a certain Kato class of the rotationally symmetric α-stable process. In this paper, we derive sharp two-sided heat kernel estimates for Lb = δα/2 + b. ∇ in D with zero exterior condition. We also obtain the boundary Harnack principle for Lb in D with explicit decay rate.",

keywords = "Boundary harnack inequality, Exit time, Gradient operator, Green function, Heat kernel, Kato class, L{\'e}vy system, Symmetric α-stable process, Transition density",

author = "Chen, {Zhen Qing} and Panki Kim and Renming Song",

year = "2012",

doi = "10.1214/11-AOP682",

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T1 - Dirichlet heat kernel estimates for fractional laplacian with gradient perturbation

AU - Chen, Zhen Qing

AU - Kim, Panki

AU - Song, Renming

PY - 2012

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N2 - Suppose that d ≥ 2 and α ∈ (1, 2). Let D be a bounded C1,1 open set in Rd and b an Rd -valued function on Rd whose components are in a certain Kato class of the rotationally symmetric α-stable process. In this paper, we derive sharp two-sided heat kernel estimates for Lb = δα/2 + b. ∇ in D with zero exterior condition. We also obtain the boundary Harnack principle for Lb in D with explicit decay rate.

AB - Suppose that d ≥ 2 and α ∈ (1, 2). Let D be a bounded C1,1 open set in Rd and b an Rd -valued function on Rd whose components are in a certain Kato class of the rotationally symmetric α-stable process. In this paper, we derive sharp two-sided heat kernel estimates for Lb = δα/2 + b. ∇ in D with zero exterior condition. We also obtain the boundary Harnack principle for Lb in D with explicit decay rate.

KW - Boundary harnack inequality

KW - Exit time

KW - Gradient operator

KW - Green function

KW - Heat kernel

KW - Kato class

KW - Lévy system

KW - Symmetric α-stable process

KW - Transition density

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DO - 10.1214/11-AOP682

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SN - 0091-1798

VL - 40

SP - 2483

EP - 2538

JO - Annals of Probability

JF - Annals of Probability

IS - 6

ER -

Dirichlet heat kernel estimates for fractional laplacian with gradient perturbation

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