The logarithmic Choquard equation : sharp asymptotics and nondegeneracy of the groundstateReport as inadecuate




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1 Département de mathématiques Université Libre de Bruxelles 2 MEPHYSTO - Quantitative methods for stochastic models in physics LPP - Laboratoire Paul Painlevé, ULB - Université Libre de Bruxelles Bruxelles, Inria Lille - Nord Europe 3 Politecnico di Bari 4 UCL IRMP - Institut de Recherche en Mathématiques et Physique

Abstract : We derive the asymptotic decay of the unique positive, radially symmetric solution to the logarithmic Choquard equation −∆u + au = 1 2π ln 1 |x| * |u| 2 u in R 2 and we establish its nondegeneracy. For the corresponding three-dimensional problem, the nondegeneracy property of the positive ground state to the Choquard equation was proved by E. Lenzmann Analysis & PDE, 2009.





Author: Denis Bonheure - Silvia Cingolani - Jean Van Schaftingen -

Source: https://hal.archives-ouvertes.fr/



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