Gradient estimates for the fundamental solution of Lévy type operator

Wei Liu; Renming Song; Longjie Xie

doi:10.1515/anona-2020-0062

Gradient estimates for the fundamental solution of Lévy type operator

Wei Liu
, Renming Song
, Longjie Xie

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

Abstract

We prove a gradient estimate and the Hölder continuity of the gradient for the fundamental solution of a class of α-stable type operators with α ∈ (0, 1), which improve known results in the literature where the condition α > 1/2 is commonly assumed.

Original language	English (US)
Pages (from-to)	1453-1462
Number of pages	10
Journal	Advances in Nonlinear Analysis
Volume	9
Issue number	1
DOIs	https://doi.org/10.1515/anona-2020-0062
State	Published - Jan 1 2020

Keywords

Lévy type operator
gradient estimate
heat kernel estimate
stochastic differential equations

ASJC Scopus subject areas

Analysis

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10.1515/anona-2020-0062

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title = "Gradient estimates for the fundamental solution of L{\'e}vy type operator",

abstract = "We prove a gradient estimate and the H{\"o}lder continuity of the gradient for the fundamental solution of a class of α-stable type operators with α ∈ (0, 1), which improve known results in the literature where the condition α > 1/2 is commonly assumed.",

keywords = "L{\'e}vy type operator, gradient estimate, heat kernel estimate, stochastic differential equations",

author = "Wei Liu and Renming Song and Longjie Xie",

note = "W. Liu is supported by NSFC (11822106, 11831014, 11571147), NSF of Jiangsu province (BK20160004) and PAPD of Jiangsu Higher Education Institutions; R. Song is supported in part by a grant from the Simons Foundation (\#429343); L. Xie is supported by NSFC (11931004) and NSF of Jiangsu province (BK20170226).",

year = "2020",

month = jan,

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doi = "10.1515/anona-2020-0062",

language = "English (US)",

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T1 - Gradient estimates for the fundamental solution of Lévy type operator

AU - Liu, Wei

AU - Song, Renming

AU - Xie, Longjie

N1 - W. Liu is supported by NSFC (11822106, 11831014, 11571147), NSF of Jiangsu province (BK20160004) and PAPD of Jiangsu Higher Education Institutions; R. Song is supported in part by a grant from the Simons Foundation (#429343); L. Xie is supported by NSFC (11931004) and NSF of Jiangsu province (BK20170226).

PY - 2020/1/1

Y1 - 2020/1/1

N2 - We prove a gradient estimate and the Hölder continuity of the gradient for the fundamental solution of a class of α-stable type operators with α ∈ (0, 1), which improve known results in the literature where the condition α > 1/2 is commonly assumed.

AB - We prove a gradient estimate and the Hölder continuity of the gradient for the fundamental solution of a class of α-stable type operators with α ∈ (0, 1), which improve known results in the literature where the condition α > 1/2 is commonly assumed.

KW - Lévy type operator

KW - gradient estimate

KW - heat kernel estimate

KW - stochastic differential equations

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DO - 10.1515/anona-2020-0062

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SP - 1453

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JO - Advances in Nonlinear Analysis

JF - Advances in Nonlinear Analysis

IS - 1

ER -

Gradient estimates for the fundamental solution of Lévy type operator

Abstract

Keywords

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