Heat kernel estimates for critical fractional diffusion operators

Longjie Xie; Xicheng Zhang

doi:10.4064/sm224-3-3

Heat kernel estimates for critical fractional diffusion operators

Longjie Xie, Xicheng Zhang

Wuhan University

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

30 Citations (Scopus)

Abstract

We construct the heat kernel of the 1=2-order Laplacian perturbed by a first-order gradient term in Hölder spaces and a zero-order potential term in a generalized Kato class, and obtain sharp two-sided estimates as well as a gradient estimate of the heat kernel, where the proof of the lower bound is based on a probabilistic approach.

Original language	English
Pages (from-to)	221-263
Number of pages	43
Journal	Studia Mathematica
Volume	224
Issue number	3
DOIs	https://doi.org/10.4064/sm224-3-3
Publication status	Published - 2014
Externally published	Yes

Keywords

Critical diffusion operator
Gradient estimate
Heat kernel estimate
Levi's method

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10.4064/sm224-3-3

Cite this

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abstract = "We construct the heat kernel of the 1=2-order Laplacian perturbed by a first-order gradient term in H{\"o}lder spaces and a zero-order potential term in a generalized Kato class, and obtain sharp two-sided estimates as well as a gradient estimate of the heat kernel, where the proof of the lower bound is based on a probabilistic approach.",

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AU - Xie, Longjie

AU - Zhang, Xicheng

N1 - Publisher Copyright: © Instytut Matematyczny PAN, 2014.

PY - 2014

Y1 - 2014

N2 - We construct the heat kernel of the 1=2-order Laplacian perturbed by a first-order gradient term in Hölder spaces and a zero-order potential term in a generalized Kato class, and obtain sharp two-sided estimates as well as a gradient estimate of the heat kernel, where the proof of the lower bound is based on a probabilistic approach.

AB - We construct the heat kernel of the 1=2-order Laplacian perturbed by a first-order gradient term in Hölder spaces and a zero-order potential term in a generalized Kato class, and obtain sharp two-sided estimates as well as a gradient estimate of the heat kernel, where the proof of the lower bound is based on a probabilistic approach.

KW - Critical diffusion operator

KW - Gradient estimate

KW - Heat kernel estimate

KW - Levi's method

UR - https://www.scopus.com/pages/publications/84919772293

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DO - 10.4064/sm224-3-3

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VL - 224

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JO - Studia Mathematica

JF - Studia Mathematica

IS - 3

ER -

Heat kernel estimates for critical fractional diffusion operators

Abstract

Keywords

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