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A class of existence results for the singular Liouville equation

TitleA class of existence results for the singular Liouville equation
Publication TypeJournal Article
Year of Publication2011
AuthorsCarlotto, A, Malchiodi, A
JournalComptes Rendus Mathematique 349 (2011) 161-166
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.

URLhttp://hdl.handle.net/1963/5793
DOI10.1016/j.crma.2010.12.016

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