We investigate existence of solutions for a singular Liouville equation on S^2 and prove sharp Onofri-type inequalities for a Moser-Trudinger functional in the presence of singular potentials. As a consequence we obtain existence of extremal functions for the Moser-Trudinger embedding on compact surfaces with conical singularities. Finally we study the blow-up behavior for sequences of solutions Liouville-type systems and prove a compactness condition which plays an important role in the variational analysis of Toda systems.
Sharp Inequalities and Blow-up Analysis for Singular Moser-Trudinger Embeddings
Mancini, Gabriele
2015
Abstract
We investigate existence of solutions for a singular Liouville equation on S^2 and prove sharp Onofri-type inequalities for a Moser-Trudinger functional in the presence of singular potentials. As a consequence we obtain existence of extremal functions for the Moser-Trudinger embedding on compact surfaces with conical singularities. Finally we study the blow-up behavior for sequences of solutions Liouville-type systems and prove a compactness condition which plays an important role in the variational analysis of Toda systems.File in questo prodotto:
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Utilizza questo identificativo per citare o creare un link a questo documento:
https://hdl.handle.net/20.500.14242/166631
Il codice NBN di questa tesi è
URN:NBN:IT:SISSA-166631