Home > Articles > Published articles > Oscillatory phenomena for higher-order fractional Laplacians |
Date: | 2024 |
Abstract: | 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. |
Rights: | Tots els drets reservats. |
Language: | Anglès |
Document: | Article ; recerca ; Versió publicada |
Subject: | Polarization inequality ; Pólya-szegö inequality ; First eigenfunction ; Positivity-preserving properties ; Faber-krahn inequality |
Published in: | Publicacions matemàtiques, Vol. 68 Núm. 1 (2024) , p. 267-286 (Articles) , ISSN 2014-4350 |
20 p, 411.1 KB |