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A class of existence results for the singular Liouville equation
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Carlotto, Alessandro and Malchiodi, A. (2011) A class of existence results for the singular Liouville equation. Comptes Rendus Mathematique, Vol.349 (No.3-4). pp. 161-166. doi:10.1016/j.crma.2010.12.016 ISSN 1631073X.
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Official URL: http://dx.doi.org/10.1016/j.crma.2010.12.016
Abstract
We consider a class of elliptic PDEs on closed surfaces with exponential nonlinearities and Dirac deltas on the right-hand side. The study arises from abelian Chern–Simons theory in self-dual regime, or from the problem of prescribing the Gaussian curvature in presence of conical singularities. A general existence result is proved using global variational methods: the analytic problem is reduced to a topological problem concerning the contractibility of a model space, the so-called space of formal barycenters, characterizing the very low sublevels of a suitable functional.
Item Type: | Journal Article | ||||
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Alternative Title: | Une classe de résultats d'existence pour l'équation de Liouville singulière | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Journal or Publication Title: | Comptes Rendus Mathematique | ||||
Publisher: | Elsevier Masson | ||||
ISSN: | 1631073X | ||||
Official Date: | 2011 | ||||
Dates: |
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Volume: | Vol.349 | ||||
Number: | No.3-4 | ||||
Page Range: | pp. 161-166 | ||||
DOI: | 10.1016/j.crma.2010.12.016 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
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