We collect some peculiarities of higher-order fractional Laplacians (-Delta)(s), s > 1, with special attention to the range s is an element of (1, 2), which show their oscillatory nature. These include the failure of the polarization and Polya-Szego inequalities and the explicit example of a domain with sign-changing first eigenfunction. In spite of these fluctuating behaviours, we prove how the Faber-Krahn inequality still holds for any s > 1 in dimension one.
Oscillatory phenomena for higher-order fractional Laplacians / Abatangelo, Nicola; Jarohs, Sven. - In: PUBLICACIONS MATEMÀTIQUES. - ISSN 0214-1493. - STAMPA. - 68:1(2024), pp. 267-286. [10.5565/PUBLMAT6812412]
Oscillatory phenomena for higher-order fractional Laplacians
Abatangelo, Nicola;
2024
Abstract
We collect some peculiarities of higher-order fractional Laplacians (-Delta)(s), s > 1, with special attention to the range s is an element of (1, 2), which show their oscillatory nature. These include the failure of the polarization and Polya-Szego inequalities and the explicit example of a domain with sign-changing first eigenfunction. In spite of these fluctuating behaviours, we prove how the Faber-Krahn inequality still holds for any s > 1 in dimension one.| File | Dimensione | Formato | |
|---|---|---|---|
|
6812412.pdf
accesso riservato
Tipo:
Versione (PDF) editoriale
Licenza:
Licenza per accesso riservato
Dimensione
411.07 kB
Formato
Adobe PDF
|
411.07 kB | Adobe PDF | Visualizza/Apri Contatta l'autore |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
