Heat kernels for time-dependent non-symmetric mixed Lévy-type operators

Zhen Qing Chen; Xicheng Zhang

doi:10.1016/j.jfa.2023.109947

Heat kernels for time-dependent non-symmetric mixed Lévy-type operators

Zhen Qing Chen^*, Xicheng Zhang

^*Corresponding author for this work

School of Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper we establish the existence, uniqueness and regularity of heat kernels to a large class of time-inhomogeneous non-symmetric nonlocal operators with Dini's continuous kernels. Moreover, quantitative estimates including two-sided estimates, gradient and fractional derivative estimates of the heat kernels are obtained.

Original language	English
Article number	109947
Journal	Journal of Functional Analysis
Volume	285
Issue number	2
DOIs	https://doi.org/10.1016/j.jfa.2023.109947
Publication status	Published - 15 Jul 2023

Keywords

Dini continuity
Heat kernel estimates
Non-symmetric nonlocal operator

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10.1016/j.jfa.2023.109947

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title = "Heat kernels for time-dependent non-symmetric mixed L{\'e}vy-type operators",

abstract = "In this paper we establish the existence, uniqueness and regularity of heat kernels to a large class of time-inhomogeneous non-symmetric nonlocal operators with Dini's continuous kernels. Moreover, quantitative estimates including two-sided estimates, gradient and fractional derivative estimates of the heat kernels are obtained.",

keywords = "Dini continuity, Heat kernel estimates, Non-symmetric nonlocal operator",

author = "Chen, {Zhen Qing} and Xicheng Zhang",

note = "Publisher Copyright: {\textcopyright} 2023 Elsevier Inc.",

year = "2023",

month = jul,

day = "15",

doi = "10.1016/j.jfa.2023.109947",

language = "English",

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AU - Chen, Zhen Qing

AU - Zhang, Xicheng

PY - 2023/7/15

Y1 - 2023/7/15

N2 - In this paper we establish the existence, uniqueness and regularity of heat kernels to a large class of time-inhomogeneous non-symmetric nonlocal operators with Dini's continuous kernels. Moreover, quantitative estimates including two-sided estimates, gradient and fractional derivative estimates of the heat kernels are obtained.

AB - In this paper we establish the existence, uniqueness and regularity of heat kernels to a large class of time-inhomogeneous non-symmetric nonlocal operators with Dini's continuous kernels. Moreover, quantitative estimates including two-sided estimates, gradient and fractional derivative estimates of the heat kernels are obtained.

KW - Dini continuity

KW - Heat kernel estimates

KW - Non-symmetric nonlocal operator

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DO - 10.1016/j.jfa.2023.109947

M3 - Article

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SN - 0022-1236

VL - 285

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

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ER -

Heat kernels for time-dependent non-symmetric mixed Lévy-type operators

Abstract

Keywords

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