Heat kernel bounds for nonlocal operators with singular kernels

Moritz Kassmann; Kyung Youn Kim; Takashi Kumagai

doi:10.1016/j.matpur.2022.05.017

Heat kernel bounds for nonlocal operators with singular kernels

Moritz Kassmann^*, Kyung Youn Kim, Takashi Kumagai

^*Corresponding author for this work

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

2 Citations (Scopus)

Abstract

We prove sharp two-sided bounds of the fundamental solution for integro-differential operators of order α∈(0,2) that generate a d-dimensional Markov process. The corresponding Dirichlet form is comparable to that of d independent copies of one-dimensional jump processes, i.e., the jumping measure is singular with respect to the d-dimensional Lebesgue measure.

Original language	English
Pages (from-to)	1-26
Number of pages	26
Journal	Journal des Mathematiques Pures et Appliquees
Volume	164
DOIs	https://doi.org/10.1016/j.matpur.2022.05.017
Publication status	Published - 2022 Aug
Externally published	Yes

Keywords

Heat kernel
Integro-differential operator
Markov jump process

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

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10.1016/j.matpur.2022.05.017

Cite this

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title = "Heat kernel bounds for nonlocal operators with singular kernels",

abstract = "We prove sharp two-sided bounds of the fundamental solution for integro-differential operators of order α∈(0,2) that generate a d-dimensional Markov process. The corresponding Dirichlet form is comparable to that of d independent copies of one-dimensional jump processes, i.e., the jumping measure is singular with respect to the d-dimensional Lebesgue measure.",

keywords = "Heat kernel, Integro-differential operator, Markov jump process",

author = "Moritz Kassmann and Kim, {Kyung Youn} and Takashi Kumagai",

note = "Funding Information: Financial support of the German Science Foundation through the International Research Training Group Bielefeld-Seoul IRTG 2235 (GRK 2235 - 282638148 ), the Alexander von Humboldt Foundation and JSPS KAKENHI Grant Number JP17H01093 are gratefully acknowledged. K.-Y. Kim is partially supported by the MOST (Ministry of Science and Technology, Taiwan) under the project MOST-110-2115-M-005-009-MY3 . Publisher Copyright: {\textcopyright} 2022",

year = "2022",

month = aug,

doi = "10.1016/j.matpur.2022.05.017",

language = "English",

volume = "164",

pages = "1--26",

journal = "Journal des Mathematiques Pures et Appliquees",

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TY - JOUR

T1 - Heat kernel bounds for nonlocal operators with singular kernels

AU - Kassmann, Moritz

AU - Kim, Kyung Youn

AU - Kumagai, Takashi

N1 - Funding Information: Financial support of the German Science Foundation through the International Research Training Group Bielefeld-Seoul IRTG 2235 (GRK 2235 - 282638148 ), the Alexander von Humboldt Foundation and JSPS KAKENHI Grant Number JP17H01093 are gratefully acknowledged. K.-Y. Kim is partially supported by the MOST (Ministry of Science and Technology, Taiwan) under the project MOST-110-2115-M-005-009-MY3 . Publisher Copyright: © 2022

PY - 2022/8

Y1 - 2022/8

N2 - We prove sharp two-sided bounds of the fundamental solution for integro-differential operators of order α∈(0,2) that generate a d-dimensional Markov process. The corresponding Dirichlet form is comparable to that of d independent copies of one-dimensional jump processes, i.e., the jumping measure is singular with respect to the d-dimensional Lebesgue measure.

AB - We prove sharp two-sided bounds of the fundamental solution for integro-differential operators of order α∈(0,2) that generate a d-dimensional Markov process. The corresponding Dirichlet form is comparable to that of d independent copies of one-dimensional jump processes, i.e., the jumping measure is singular with respect to the d-dimensional Lebesgue measure.

KW - Heat kernel

KW - Integro-differential operator

KW - Markov jump process

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DO - 10.1016/j.matpur.2022.05.017

M3 - Article

AN - SCOPUS:85132953610

SN - 0021-7824

VL - 164

SP - 1

EP - 26

JO - Journal des Mathematiques Pures et Appliquees

JF - Journal des Mathematiques Pures et Appliquees

ER -

Heat kernel bounds for nonlocal operators with singular kernels

Abstract

Keywords

ASJC Scopus subject areas

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