Symmetry of extremals of functional inequalities via spectral estimates for linear operators

TL;DR

This paper establishes new symmetry properties of extremal functions for a class of functional inequalities in higher dimensions, using spectral estimates for linear operators, expanding the understanding of symmetry in these mathematical contexts.

Contribution

It introduces novel symmetry results for extremals of Caffarelli-Kohn-Nirenberg inequalities in dimensions ≥2, based on spectral estimates where no explicit symmetry results were previously known.

Findings

New symmetry results for extremals in higher dimensions

Applicable to a range of parameters without explicit symmetry

Advances understanding of functional inequality extremals

Abstract

We prove new symmetry results for the extremals of the Caffarelli-Kohn-Nirenberg inequalities in any dimension larger or equal than 2, in a range of parameters for which no explicit results of symmetry were previously known.