The logarithmic Choquard equation : sharp ...
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]
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 >
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 :
Source :
Files
- document
- Open access
- Access the document
- 1612.02194.pdf
- Open access
- Access the document
- document
- Open access
- Access the document
- 1612.02194.pdf
- Open access
- Access the document