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Multiplicity results for the assigned Gauss curvature problem in R2

dc.contributor.authorTarantello, Gabriella
dc.contributor.authorEsteban, Maria J.
HAL ID: 738381
ORCID: 0000-0003-1700-9338
dc.contributor.authorDolbeault, Jean
HAL ID: 87
ORCID: 0000-0003-4234-2298
dc.date.accessioned2009-07-03T08:28:03Z
dc.date.available2009-07-03T08:28:03Z
dc.date.issued2009
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/718
dc.language.isoenen
dc.subjectSelf-dual gauge field vortices
dc.subjectOnsager equation
dc.subjectLiouville equation
dc.subjectRiemannian manifolds
dc.subjectConical singularities
dc.subjectGauss curvatureen
dc.subjectMultiplicity
dc.subjectUniqueness
dc.subjectRadial symmetry
dc.subjectBlow-up
dc.subjectEmden–Fowler transformation
dc.subjectStereographic projection
dc.subject.ddc519en
dc.titleMultiplicity results for the assigned Gauss curvature problem in R2en
dc.typeArticle accepté pour publication ou publié
dc.contributor.editoruniversityotherUniversita degli studi di Roma II;Italie
dc.description.abstractenTo 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.en
dc.relation.isversionofjnlnameNonlinear Analysis: Theory, Methods & Applications
dc.relation.isversionofjnlvol70
dc.relation.isversionofjnlissue8
dc.relation.isversionofjnldate2009-04
dc.relation.isversionofjnldate2009
dc.relation.isversionofjnlpages2870-2881
dc.relation.isversionofdoihttp://dx.doi.org/10.1016/j.na.2008.12.040
dc.identifier.urlsitehttp://hal.archives-ouvertes.fr/hal-00323700/en/en
dc.description.sponsorshipprivateouien
dc.relation.isversionofjnlpublisherElsevier
dc.subject.ddclabelProbabilités et Mathématiques appliquéesen


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