Upper heat kernel estimates for nonlocal operators via Aronson’s method

Kaßmann, Moritz; Weidner, Marvin

Upper heat kernel estimates for nonlocal operators via Aronson’s method

Kaßmann M, Weidner M (2023)
Calculus of Variations and Partial Differential Equations 62(2): 68.

Zeitschriftenaufsatz | Veröffentlicht | Englisch

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DOI

https://doi.org/10.1007/s00526-022-02398-y

URN

urn:nbn:de:0070-pub-29680305

Autor*in

Kaßmann, Moritz^UniBi ; Weidner, Marvin

Einrichtung

Fakultät für Mathematik

Abstract / Bemerkung

In his celebrated article, Aronson established Gaussian bounds for the fundamental solution to the Cauchy problem governed by a second order divergence form operator with uniformly elliptic coefficients. We extend Aronson’s proof of upper heat kernel estimates to nonlocal operators whose jumping kernel satisfies a pointwise upper bound and whose energy form is coercive. A detailed proof is given in the Euclidean space and extensions to doubling metric measure spaces are discussed.

Erscheinungsjahr

2023

Zeitschriftentitel

Calculus of Variations and Partial Differential Equations

Band

Ausgabe

Art.-Nr.

Urheberrecht / Lizenzen

Creative Commons Namensnennung 4.0 International Public License (CC-BY 4.0)

ISSN

0944-2669

eISSN

1432-0835

Finanzierungs-Informationen

Open-Access-Publikationskosten wurden durch die Universität Bielefeld im Rahmen des DEAL-Vertrags gefördert.

Page URI

https://pub.uni-bielefeld.de/record/2968030

Zitieren

Kaßmann M, Weidner M. Upper heat kernel estimates for nonlocal operators via Aronson’s method. Calculus of Variations and Partial Differential Equations. 2023;62(2): 68.

Kaßmann, M., & Weidner, M. (2023). Upper heat kernel estimates for nonlocal operators via Aronson’s method. Calculus of Variations and Partial Differential Equations, 62(2), 68. https://doi.org/10.1007/s00526-022-02398-y

Kaßmann, Moritz, and Weidner, Marvin. 2023. “Upper heat kernel estimates for nonlocal operators via Aronson’s method”. Calculus of Variations and Partial Differential Equations 62 (2): 68.

Kaßmann, M., and Weidner, M. (2023). Upper heat kernel estimates for nonlocal operators via Aronson’s method. Calculus of Variations and Partial Differential Equations 62:68.

Kaßmann, M., & Weidner, M., 2023. Upper heat kernel estimates for nonlocal operators via Aronson’s method. Calculus of Variations and Partial Differential Equations, 62(2): 68.

M. Kaßmann and M. Weidner, “Upper heat kernel estimates for nonlocal operators via Aronson’s method”, Calculus of Variations and Partial Differential Equations, vol. 62, 2023, : 68.

Kaßmann, M., Weidner, M.: Upper heat kernel estimates for nonlocal operators via Aronson’s method. Calculus of Variations and Partial Differential Equations. 62, : 68 (2023).

Kaßmann, Moritz, and Weidner, Marvin. “Upper heat kernel estimates for nonlocal operators via Aronson’s method”. Calculus of Variations and Partial Differential Equations 62.2 (2023): 68.

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