Oscillatory phenomena for higher-order fractional Laplacians
Abatangelo, Nicola (Università di Bologna. Dipartimento di Matematica)
Jarohs, Sven (Goethe-Universität Frankfurt am Main. Institut für Mathematik)

Data:	2024
Resum:	We collect some peculiarities of higher-order fractional Laplacians (−∆)s , s > 1, with special attention to the range s ∈ (1, 2), which show their oscillatory nature. These include the failure of the polarization and P'olya-Szeg˝o 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.
Drets:	Tots els drets reservats.
Llengua:	Anglès
Document:	Article ; recerca ; Versió publicada
Matèria:	Polarization inequality ; Pólya-szegö inequality ; First eigenfunction ; Positivity-preserving properties ; Faber-krahn inequality
Publicat a:	Publicacions matemàtiques, Vol. 68 Núm. 1 (2024) , p. 267-286 (Articles) , ISSN 2014-4350

Adreça original: https://raco.cat/index.php/PublicacionsMatematiques/article/view/422945
DOI: 10.5565/PUBLMAT6812412

20 p, 411.1 KB

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