On uniqueness and non-degeneracy of anisotropic polarons
Ricaud, Julien (2016), On uniqueness and non-degeneracy of anisotropic polarons, Nonlinearity, 29, 5, p. n°1507. 10.1088/0951-7715/29/5/1507
TypeArticle accepté pour publication ou publié
External document linkhttps://arxiv.org/abs/1412.1230v1
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Abstract (EN)We study the anisotropic Choquard–Pekar equation which de-scribes 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.
Subjects / KeywordsAnisotropic polarons; anisotropic Choquard–Pekar equation
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