The logarithmic Choquard equation : sharp asymptotics and nondegeneracy of the groundstate

Bonheure, Denis; Cingolani, Silvia; van Schaftingen, Jean

Document type :

Pré-publication ou Document de travail

Title :

The logarithmic Choquard equation : sharp asymptotics and nondegeneracy of the groundstate

Author(s) :

Bonheure, Denis [Auteur]
Quantitative methods for stochastic models in physics [MEPHYSTO]
Département de mathématiques Université Libre de Bruxelles
Cingolani, Silvia [Auteur]
Polytechnic University of Bari / Politecnico di Bari
van Schaftingen, Jean [Auteur]
Institut de Recherche en Mathématiques et Physique [UCL IRMP]

HAL domain(s) :

Mathématiques [math]/Equations aux dérivées partielles [math.AP]

English abstract : [en]

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 ...
Show more >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).Show less >

Language :

Anglais

Collections :