Sharp heat kernel estimates for spectral fractional Laplacian perturbed by gradients

Renming Song; Longjie Xie; Yingchao Xie

doi:10.1007/s11425-018-9472-x

Sharp heat kernel estimates for spectral fractional Laplacian perturbed by gradients

Renming Song, Longjie Xie, Yingchao Xie

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

Abstract

Using Duhamel’s formula, we prove sharp two-sided estimates for the spectral fractional Laplacian’s heat kernel with time-dependent gradient perturbation in bounded C^1,1 domains. In addition, we obtain a gradient estimate as well as the Hölder continuity of the heat kernel’s gradient.

Original language	English (US)
Pages (from-to)	2343-2362
Number of pages	20
Journal	Science China Mathematics
Volume	63
Issue number	11
DOIs	https://doi.org/10.1007/s11425-018-9472-x
State	Published - Nov 1 2020

Keywords

60J35
60J50
Dirichlet heat kernel
Kato class
gradient estimate
spectral fractional Laplacian

ASJC Scopus subject areas

General Mathematics

Online availability

10.1007/s11425-018-9472-x

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title = "Sharp heat kernel estimates for spectral fractional Laplacian perturbed by gradients",

abstract = "Using Duhamel{\textquoteright}s formula, we prove sharp two-sided estimates for the spectral fractional Laplacian{\textquoteright}s heat kernel with time-dependent gradient perturbation in bounded C1,1 domains. In addition, we obtain a gradient estimate as well as the H{\"o}lder continuity of the heat kernel{\textquoteright}s gradient.",

keywords = "60J35, 60J50, Dirichlet heat kernel, Kato class, gradient estimate, spectral fractional Laplacian",

author = "Renming Song and Longjie Xie and Yingchao Xie",

note = "Publisher Copyright: {\textcopyright} 2020, Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature.",

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doi = "10.1007/s11425-018-9472-x",

language = "English (US)",

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AU - Song, Renming

AU - Xie, Longjie

AU - Xie, Yingchao

PY - 2020/11/1

Y1 - 2020/11/1

N2 - Using Duhamel’s formula, we prove sharp two-sided estimates for the spectral fractional Laplacian’s heat kernel with time-dependent gradient perturbation in bounded C1,1 domains. In addition, we obtain a gradient estimate as well as the Hölder continuity of the heat kernel’s gradient.

AB - Using Duhamel’s formula, we prove sharp two-sided estimates for the spectral fractional Laplacian’s heat kernel with time-dependent gradient perturbation in bounded C1,1 domains. In addition, we obtain a gradient estimate as well as the Hölder continuity of the heat kernel’s gradient.

KW - 60J35

KW - 60J50

KW - Dirichlet heat kernel

KW - Kato class

KW - gradient estimate

KW - spectral fractional Laplacian

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ER -

Sharp heat kernel estimates for spectral fractional Laplacian perturbed by gradients

Abstract

Keywords

ASJC Scopus subject areas

Online availability

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