Heat Kernel Estimates for Non-symmetric Finite Range Jump Processes

Jie Ming Wang

doi:10.1007/s10114-020-9459-1

Heat Kernel Estimates for Non-symmetric Finite Range Jump Processes

Jie Ming Wang^*

^*此作品的通讯作者

数学学院

科研成果: 期刊稿件 › 文章 › 同行评审

摘要

In this paper, we first establish the sharp two-sided heat kernel estimates and the gradient estimate for the truncated fractional Laplacian under gradient perturbation S^b= Δ ¯ ^α^/²+ b⋅ ∇ where Δ ¯ ^α^/² is the truncated fractional Laplacian, α ∈ (1, 2) and b ∈ K_d^α−1. In the second part, for a more general finite range jump process, we present some sufficient conditions to allow that the two sided estimates of the heat kernel are comparable to the Poisson type function for large distance ∣x − y∣ in short time.

源语言	英语
页（从-至）	229-248
页数	20
期刊	Acta Mathematica Sinica, English Series
卷	37
期	2
DOI	https://doi.org/10.1007/s10114-020-9459-1
出版状态	已出版 - 2月 2021

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title = "Heat Kernel Estimates for Non-symmetric Finite Range Jump Processes",

abstract = "In this paper, we first establish the sharp two-sided heat kernel estimates and the gradient estimate for the truncated fractional Laplacian under gradient perturbation Sb= Δ ¯ α/2+ b⋅ ∇ where Δ ¯ α/2 is the truncated fractional Laplacian, α ∈ (1, 2) and b ∈ Kdα−1. In the second part, for a more general finite range jump process, we present some sufficient conditions to allow that the two sided estimates of the heat kernel are comparable to the Poisson type function for large distance ∣x − y∣ in short time.",

keywords = "47D07, 47G20, 60J35, 60J75, Heat kernel, finite range jump process, gradient estimate, martingale problem, transition density function, truncated fractional Laplacian",

author = "Wang, \{Jie Ming\}",

note = "Publisher Copyright: {\textcopyright} 2020, Springer-Verlag GmbH Germany \& The Editorial Office of AMS.",

year = "2021",

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doi = "10.1007/s10114-020-9459-1",

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T1 - Heat Kernel Estimates for Non-symmetric Finite Range Jump Processes

AU - Wang, Jie Ming

PY - 2021/2

Y1 - 2021/2

N2 - In this paper, we first establish the sharp two-sided heat kernel estimates and the gradient estimate for the truncated fractional Laplacian under gradient perturbation Sb= Δ ¯ α/2+ b⋅ ∇ where Δ ¯ α/2 is the truncated fractional Laplacian, α ∈ (1, 2) and b ∈ Kdα−1. In the second part, for a more general finite range jump process, we present some sufficient conditions to allow that the two sided estimates of the heat kernel are comparable to the Poisson type function for large distance ∣x − y∣ in short time.

AB - In this paper, we first establish the sharp two-sided heat kernel estimates and the gradient estimate for the truncated fractional Laplacian under gradient perturbation Sb= Δ ¯ α/2+ b⋅ ∇ where Δ ¯ α/2 is the truncated fractional Laplacian, α ∈ (1, 2) and b ∈ Kdα−1. In the second part, for a more general finite range jump process, we present some sufficient conditions to allow that the two sided estimates of the heat kernel are comparable to the Poisson type function for large distance ∣x − y∣ in short time.

KW - 47D07

KW - 47G20

KW - 60J35

KW - 60J75

KW - Heat kernel

KW - finite range jump process

KW - gradient estimate

KW - martingale problem

KW - transition density function

KW - truncated fractional Laplacian

UR - https://www.scopus.com/pages/publications/85097195914

U2 - 10.1007/s10114-020-9459-1

DO - 10.1007/s10114-020-9459-1

M3 - Article

AN - SCOPUS:85097195914

SN - 1439-8516

VL - 37

SP - 229

EP - 248

JO - Acta Mathematica Sinica, English Series

JF - Acta Mathematica Sinica, English Series

IS - 2

ER -

Heat Kernel Estimates for Non-symmetric Finite Range Jump Processes

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