Rigidity for the P\'olya-Szeg\"o inequality under circular rearrangement
F. Cagnetti, G. Domazakis, M. Perugini, F. Seuffert
TL;DR
This paper proves a Pólya-Szegö inequality for circular rearrangement under broad conditions and identifies when extremals are symmetric.
Contribution
It establishes a general Pólya-Szegö inequality for circular rearrangement and provides conditions for symmetry of extremals.
Findings
Proved a Pólya-Szegö inequality for circular rearrangement.
Identified conditions ensuring extremals are symmetric.
Abstract
A P\'olya-Szeg\"o inequality for the circular rearrangement is proven, under general assumptions. In addition, sufficient conditions are given, under which all the extremals of the inequality are symmetric.
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