We apply the results established in [12] to prove some new fractional Leibniz rules involving BVα,p and Sα,p functions, following the distributional approach adopted in the previous works [8,13,14]. In order to achieve our main results, we revise the elementary properties of the fractional operators involved in the framework of Besov spaces and we rephraze the Kenig–Ponce–Vega Leibniz-type rule in our fractional context. We apply our results to prove the well-posedness of the boundary-value problem for a general 2α-order fractional elliptic operator in divergence form.
Leibniz rules and Gauss–Green formulas in distributional fractional spaces / Comi G.E.; Stefani G.. - In: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS. - ISSN 0022-247X. - STAMPA. - 514:2(2022), pp. 126312.1-126312.41. [10.1016/j.jmaa.2022.126312]
Leibniz rules and Gauss–Green formulas in distributional fractional spaces
Comi G. E.;
2022
Abstract
We apply the results established in [12] to prove some new fractional Leibniz rules involving BVα,p and Sα,p functions, following the distributional approach adopted in the previous works [8,13,14]. In order to achieve our main results, we revise the elementary properties of the fractional operators involved in the framework of Besov spaces and we rephraze the Kenig–Ponce–Vega Leibniz-type rule in our fractional context. We apply our results to prove the well-posedness of the boundary-value problem for a general 2α-order fractional elliptic operator in divergence form.File | Dimensione | Formato | |
---|---|---|---|
Comi_Stefani_Leibniz_rules_and_Gauss_Green_formulas.pdf
embargo fino al 10/05/2024
Tipo:
Postprint
Licenza:
Licenza per Accesso Aperto. Creative Commons Attribuzione - Non commerciale - Non opere derivate (CCBYNCND)
Dimensione
806.02 kB
Formato
Adobe PDF
|
806.02 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.