The Harnack inequality fails for nonlocal kinetic equations
Kaßmann M, Weidner M (2024)
Advances in Mathematics 459: 110030.
Zeitschriftenaufsatz
| Veröffentlicht | Englisch
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Autor*in
Kaßmann, MoritzUniBi 
;
Weidner, Marvin
;
Weidner, MarvinEinrichtung
Abstract / Bemerkung
We prove that the Harnack inequality fails for nonlocal kinetic equations. Such equations arise as linearized models for the Boltzmann equation without cutoff and are of hypoelliptic type. We provide a counterexample for the simplest equation in this theory, the fractional Kolmogorov equation. Our result reflects a purely nonlocal phenomenon since the Harnack inequality holds true for local kinetic equations like the Kolmogorov equation. (c) 2024 Published by Elsevier Inc.
Stichworte
Nonlocal;
Fractional;
Harnack
Erscheinungsjahr
2024
Zeitschriftentitel
Advances in Mathematics
Band
459
Art.-Nr.
110030
ISSN
0001-8708
eISSN
1090-2082
Page URI
https://pub.uni-bielefeld.de/record/2999527
Zitieren
Kaßmann M, Weidner M. The Harnack inequality fails for nonlocal kinetic equations. Advances in Mathematics. 2024;459: 110030.
Kaßmann, M., & Weidner, M. (2024). The Harnack inequality fails for nonlocal kinetic equations. Advances in Mathematics, 459, 110030. https://doi.org/10.1016/j.aim.2024.110030
Kaßmann, Moritz, and Weidner, Marvin. 2024. “The Harnack inequality fails for nonlocal kinetic equations”. Advances in Mathematics 459: 110030.
Kaßmann, M., and Weidner, M. (2024). The Harnack inequality fails for nonlocal kinetic equations. Advances in Mathematics 459:110030.
Kaßmann, M., & Weidner, M., 2024. The Harnack inequality fails for nonlocal kinetic equations. Advances in Mathematics, 459: 110030.
M. Kaßmann and M. Weidner, “The Harnack inequality fails for nonlocal kinetic equations”, Advances in Mathematics, vol. 459, 2024, : 110030.
Kaßmann, M., Weidner, M.: The Harnack inequality fails for nonlocal kinetic equations. Advances in Mathematics. 459, : 110030 (2024).
Kaßmann, Moritz, and Weidner, Marvin. “The Harnack inequality fails for nonlocal kinetic equations”. Advances in Mathematics 459 (2024): 110030.
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