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September 30, 2025Open Access

The Polya-Szego principle in the fractional setting: a glimpse on nonlocal functional inequalities

Key Points

The fractional Polya-Szego principle shows strong results in nonlocal functional inequalities, enhancing our understanding of symmetrization techniques.
Symmetrization methods in the fractional setting provide sharp results, including various isoperimetric type inequalities that demonstrate significance in analysis.
Further developments discuss stability issues and generalizations in both the anisotropic and Gaussian settings to broaden the scope of the principle.
The study emphasizes the importance of nonlocal functional inequalities in contemporary mathematical analysis and potential applications.

Abstract

In this survey we present the fractional Polya Szego 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.

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Alessandro Carbotti (Mon,) studied this question.

synapsesocial.com/papers/68dc12cc8a7d58c25ebb0c6a https://doi.org/https://doi.org/10.48550/arxiv.2509.12023