On uniqueness and non-degeneracy of anisotropic polarons

被引：4
|
作者：
Ricaud, Julien [1 ,2 ]
机构：
[1] Univ Cergy Pontoise, CNRS, Math Dept UMR 8088, F-95000 Cergy Pontoise, France
[2] Univ Paris 09, CNRS, CEREMADE UMR 7534, F-75016 Paris, France
来源：
NONLINEARITY | 2016年 / 29卷 / 05期
基金：
欧洲研究理事会;
关键词：
Choquard-Pekar; polaron; linearized operator; non-degeneracy; CONCENTRATION-COMPACTNESS PRINCIPLE; EXISTENCE; CALCULUS; SYMMETRY; STATES;
D O I：
10.1088/0951-7715/29/5/1507
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study the anisotropic Choquard-Pekar equation which describes a polaron in an anisotropic medium. We prove the uniqueness and non-degeneracy of minimizers in a weakly anisotropic medium. In addition, for a wide range of anisotropic media, we derive the symmetry properties of minimizers and prove that the kernel of the associated linearized operator is reduced, apart from three functions coming from the translation invariance, to the kernel on the subspace of functions that are even in each of the three principal directions of the medium.
引用
收藏
页码：1507 / 1536
页数：30
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