Uniqueness for fractional parabolic and elliptic equations with drift
Meglioli G, Punzo F (2023)
Communications on Pure and Applied Analysis.
Zeitschriftenaufsatz
| E-Veröff. vor dem Druck | Englisch
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Autor*in
Meglioli, GiuliaUniBi;
Punzo, Fabio
Einrichtung
Abstract / Bemerkung
We investigate uniqueness, in suitable weighted Lebesgue spaces, of solutions to a class of linear, nonlocal parabolic problems with a drift. More precisely, the problem is nonlocal due to the presence of the fractional Laplacian as diffusion operator. The drift term is driven by a smooth enough, possibly unbounded vector field b which satisfies a suitable growth condition in the set {x is an element of RN : ⟨b(x), x⟩ > 0}. In general, our uniqueness class includes unbounded solutions; in particular, we get uniqueness of bounded solutions. Furthermore, we show sharpness of the hypothesis on the drift term b; in fact we show that, if the drift term b violates, in an appropriate sense, the mentioned growth con-dition (see (2.5)), then infinitely many bounded solutions to the problem exist. Finally, we also investigate uniqueness of a linear, nonlocal elliptic equation with a drift term obtaining similar results.
Stichworte
Fractional Laplacian;
equations with drift;
uniqueness;
weighted;
Lebesgue spaces;
non-uniqueness
Erscheinungsjahr
2023
Zeitschriftentitel
Communications on Pure and Applied Analysis
ISSN
1534-0392
eISSN
1553-5258
Page URI
https://pub.uni-bielefeld.de/record/2979030
Zitieren
Meglioli G, Punzo F. Uniqueness for fractional parabolic and elliptic equations with drift. Communications on Pure and Applied Analysis. 2023.
Meglioli, G., & Punzo, F. (2023). Uniqueness for fractional parabolic and elliptic equations with drift. Communications on Pure and Applied Analysis. https://doi.org/10.3934/cpaa.2023054
Meglioli, Giulia, and Punzo, Fabio. 2023. “Uniqueness for fractional parabolic and elliptic equations with drift”. Communications on Pure and Applied Analysis.
Meglioli, G., and Punzo, F. (2023). Uniqueness for fractional parabolic and elliptic equations with drift. Communications on Pure and Applied Analysis.
Meglioli, G., & Punzo, F., 2023. Uniqueness for fractional parabolic and elliptic equations with drift. Communications on Pure and Applied Analysis.
G. Meglioli and F. Punzo, “Uniqueness for fractional parabolic and elliptic equations with drift”, Communications on Pure and Applied Analysis, 2023.
Meglioli, G., Punzo, F.: Uniqueness for fractional parabolic and elliptic equations with drift. Communications on Pure and Applied Analysis. (2023).
Meglioli, Giulia, and Punzo, Fabio. “Uniqueness for fractional parabolic and elliptic equations with drift”. Communications on Pure and Applied Analysis (2023).
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