Journal
NONLINEARITY
Volume 29, Issue 5, Pages 1507-1536Publisher
IOP Publishing Ltd
DOI: 10.1088/0951-7715/29/5/1507
Keywords
Choquard-Pekar; polaron; linearized operator; non-degeneracy
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Funding
- European Research Council under the European Community's Seventh Framework Programme (FP7) [MNIQS 258023]
- French ministry of research [ANR-10-BLAN-0101]
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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.
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