ETD system

Electronic theses and dissertations repository

 

Tesi etd-06092010-101512


Thesis type
Tesi di laurea specialistica
Author
CARLOTTO, ALESSANDRO
URN
etd-06092010-101512
Title
A class of existence results for the singular Liouville equation
Struttura
SCIENZE MATEMATICHE, FISICHE E NATURALI
Corso di studi
MATEMATICA
Commissione
relatore Prof. Malchiodi, Andrea
Parole chiave
  • Min-max Schemes
  • Variational Methods
  • Geometric PDEs
  • Blow-up analysis
Data inizio appello
16/07/2010;
Consultabilità
parziale
Data di rilascio
16/07/2050
Riassunto analitico
We consider a class of elliptic PDEs on closed surfaces with exponential nonliearities 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.<br><br>A general existence result is proved using global variational methods and some examples of application are studied in detail. The analytic problem is reduced to a topological problem concerning the contractibility of a model space associated to the equation, the so-called space of formal baricenters. Finally, a conjecture is presented in order to reduce such topological investigation to test a very simple algebraic relation involving the parameters that appear in the equation.
File