On the supercritical fractional diffusion equation with Hardy-type drift

On the supercritical fractional diffusion equation with Hardy-type drift

We study the heat kernel of the supercritical fractional diffusion equation with the drift in the critical Hölder space. We show that such a drift can have point irregularities strong enough to make the heat kernel vanish at a point for all t > 0.

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Veröffentlicht in:Journal d'analyse mathématique (Jerusalem) 2024-04, Vol.152 (2), p.401-420
Hauptverfasser: Kinzebulatov, Damir, Madou, Kodjo Raphaël, Semënov, Yuliy A.
Format: Artikel
Sprache:eng
Schlagworte:
Abstract Harmonic Analysis
Analysis
Drift
Dynamical Systems and Ergodic Theory
Functional Analysis
Mathematics
Mathematics and Statistics
Partial Differential Equations
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Zusammenfassung:We study the heat kernel of the supercritical fractional diffusion equation with the drift in the critical Hölder space. We show that such a drift can have point irregularities strong enough to make the heat kernel vanish at a point for all t > 0.
ISSN:0021-7670
1565-8538
DOI:10.1007/s11854-023-0300-5