Interpolation inequalities on the sphere and phase transition: rigidity, symmetry and symmetry breaking

2022/10/30 by Esther Bou Dagher, Jean Dolbeault, Dagher, Esther Bou +1
Computer Science · Engineering · Mathematics · #26D10 #35B06 #58J05 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2210.16878

openalex publication_date 2022/10/30 · openalex created_date 2022/11/06 · openalex updated_date 2026/07/28

Abstract

This paper is devoted to the study of phase transitions associated to a large family of Gagliardo-Nirenberg-Sobolev interpolation inequalities on the sphere depending on one parameter. We characterize symmetry and symmetry breaking regimes, with a phase transition that can be of first or second order. We establish various new results and study the qualitative properties of the branches of solutions to the Euler-Lagrange equations.

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