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Multiplicity results for the assigned Gauss curvature problem in R2

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Date
2009
Link to item file
http://hal.archives-ouvertes.fr/hal-00323700/en/
Dewey
Probabilités et Mathématiques appliquées
Sujet
Self-dual gauge field vortices; Onsager equation; Liouville equation; Riemannian manifolds; Conical singularities; Gauss curvature; Multiplicity; Uniqueness; Radial symmetry; Blow-up; Emden–Fowler transformation; Stereographic projection
Journal issue
Nonlinear Analysis: Theory, Methods & Applications
Volume
70
Number
8
Publication date
04-2009
Article pages
2870-2881
Publisher
Elsevier
DOI
http://dx.doi.org/10.1016/j.na.2008.12.040
URI
https://basepub.dauphine.fr/handle/123456789/718
Collections
  • CEREMADE : Publications
Metadata
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Author
Tarantello, Gabriella
Esteban, Maria J.
Dolbeault, Jean
Type
Article accepté pour publication ou publié
Abstract (EN)
To study the problem of the assigned Gauss curvature with conical singularities on Riemanian manifolds, we consider the Liouville equation with a single Dirac measure on the two-dimensional sphere. By a stereographic projection, we reduce the problem to a Liouville equation on the euclidean plane. We prove new multiplicity results for bounded radial solutions, which improve on earlier results of C.-S. Lin and his collaborators. Based on numerical computations, we also present various conjectures on the number of unbounded solutions. Using symmetries, some multiplicity results for non radial solutions are also stated.

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