Heat kernel estimates for the Dirichlet fractional Laplacian

Zhen Qing Chen; Panki Kim; Renming Song

doi:10.4171/JEMS/231

Heat kernel estimates for the Dirichlet fractional Laplacian

Zhen Qing Chen^*, Panki Kim, Renming Song

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科研成果: 期刊稿件 › 文章 › 同行评审

162 引用（Scopus）

摘要

We consider the fractional Laplacian - (-Δ) ^α/2 on an open subset in 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 α-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.

源语言	英语
页（从-至）	1307-1327
页数	21
期刊	Journal of the European Mathematical Society
卷	12
期	5
DOI	https://doi.org/10.4171/JEMS/231
出版状态	已出版 - 2010
已对外发布	是

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Chen, Z. Q., Kim, P., & Song, R. (2010). Heat kernel estimates for the Dirichlet fractional Laplacian. Journal of the European Mathematical Society, 12(5), 1307-1327. https://doi.org/10.4171/JEMS/231

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title = "Heat kernel estimates for the Dirichlet fractional Laplacian",

abstract = "We consider the fractional Laplacian - (-Δ) α/2 on an open subset in 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 α-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.",

keywords = "Boundary harnack inequality, Exit time, Fractional Laplacian, Green function, Heat kernel, Intrinsic ultracontractivity, L{\'e}vy system, Parabolic harnack inequality, Symmetric α-stable process, Transition density",

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

year = "2010",

doi = "10.4171/JEMS/231",

language = "English",

volume = "12",

pages = "1307--1327",

journal = "Journal of the European Mathematical Society",

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T1 - Heat kernel estimates for the Dirichlet fractional Laplacian

AU - Chen, Zhen Qing

AU - Kim, Panki

AU - Song, Renming

PY - 2010

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N2 - We consider the fractional Laplacian - (-Δ) α/2 on an open subset in 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 α-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.

AB - We consider the fractional Laplacian - (-Δ) α/2 on an open subset in 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 α-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.

KW - Boundary harnack inequality

KW - Exit time

KW - Fractional Laplacian

KW - Green function

KW - Heat kernel

KW - Intrinsic ultracontractivity

KW - Lévy system

KW - Parabolic harnack inequality

KW - Symmetric α-stable process

KW - Transition density

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U2 - 10.4171/JEMS/231

DO - 10.4171/JEMS/231

M3 - Article

AN - SCOPUS:77955474529

SN - 1435-9855

VL - 12

SP - 1307

EP - 1327

JO - Journal of the European Mathematical Society

JF - Journal of the European Mathematical Society

IS - 5

ER -

Heat kernel estimates for the Dirichlet fractional Laplacian

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