Accepted Paper

Inserted: 12 sep 2025
Last Updated: 24 feb 2026

Journal: To appear as bookchapter in "New Frontiers in Homogenization and Fractional Calculus"
Pages: 24
Year: 2026

Abstract:

In this bookchapter we present the fractional Pólya–Szegö principle and its main consequences in the study of nonlocal functional inequalities. In particular, we show how symmetrization methods work also in the fractional setting and yield sharp results such as isoperimetric type inequalities. Further developments including stability issues and generalizations in the anisotropic and the Gaussian setting are also discussed.

Keywords: functional inequalities, Fractional seminorms, Schwarz Rearrangement, Pólya-Szegö principle

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• Bookchapter_Carbotti.pdf