We face a rigidity problem for the fractional $p$-Laplace operator to extend to this new framework some tools useful for the linear case. It is known that $(-Delta)^s(1-|x|^{2})^s_+$ and $-Delta_p(1-|x|^{rac{p}{p-1}})$ are constant functions in $(-1,1)$ for fixed $p$ and $s$. We evaluated $(-Delta_p)^s(1-|x|^{rac{p}{p-1}})^s_+$ proving that it is not constant in $(-1,1)$ for some $pin (1,+infty)$ and $sin (0,1)$. This conclusion is obtained numerically thanks to the use of very accurate Gaussian numerical quadrature formulas.
Some evaluations of the fractional p-Laplace operator on radial functions / Francesca Colasuonno, Fausto Ferrari, Paola Gervasio, Alfio Quarteroni. - In: MATHEMATICS IN ENGINEERING. - ISSN 2640-3501. - STAMPA. - 5:1(2022), pp. 1-23. [10.3934/mine.2023015]
Some evaluations of the fractional p-Laplace operator on radial functions
Francesca Colasuonno;Fausto Ferrari
;
2022
Abstract
We face a rigidity problem for the fractional $p$-Laplace operator to extend to this new framework some tools useful for the linear case. It is known that $(-Delta)^s(1-|x|^{2})^s_+$ and $-Delta_p(1-|x|^{rac{p}{p-1}})$ are constant functions in $(-1,1)$ for fixed $p$ and $s$. We evaluated $(-Delta_p)^s(1-|x|^{rac{p}{p-1}})^s_+$ proving that it is not constant in $(-1,1)$ for some $pin (1,+infty)$ and $sin (0,1)$. This conclusion is obtained numerically thanks to the use of very accurate Gaussian numerical quadrature formulas.File | Dimensione | Formato | |
---|---|---|---|
10.3934_mine.2023015-ONLINE.pdf
accesso aperto
Tipo:
Versione (PDF) editoriale
Licenza:
Creative commons
Dimensione
573.05 kB
Formato
Adobe PDF
|
573.05 kB | Adobe PDF | Visualizza/Apri |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.