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arXiv · 2210.16878

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

Esther Bou Dagher·Jean Dolbeault
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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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Esther Bou Dagher, Jean Dolbeault. 2022-10-30. Interpolation inequalities on the sphere and phase transition: rigidity, symmetry and symmetry breaking. https://arxiv.org/abs/2210.16878

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