Oscillatory phenomena for higher-order fractional Laplacians

• Autores: Nicola Abatangelo, Sven Jarohs
• Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 68, Nº. 1, 2024, págs. 267-286
• Idioma: inglés
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• Resumen

  • 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.