We consider a class of singular Liouville equations on compact surfaces motivated by the study of Electroweak and Self-Dual Chern-Simons theories, the Gaussian curvature prescription with conical singularities and Onsager's description of turbulence. We analyse the problem of existence variationally, and show how the angular distribution of the conformal volume near the singularities may lead to improvements in the Moser-Trudinger inequality, and in turn to lower bounds on the Euler-Lagrange functional. We then discuss existence and non-existence results.

Bartolucci, D., Malchiodi, A. (2013). An Improved Geometric Inequality via Vanishing Moments, with Applications to Singular Liouville Equations. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 322(2), 415-452 [10.1007/s00220-013-1731-0].

An Improved Geometric Inequality via Vanishing Moments, with Applications to Singular Liouville Equations

BARTOLUCCI, DANIELE;
2013-01-01

Abstract

We consider a class of singular Liouville equations on compact surfaces motivated by the study of Electroweak and Self-Dual Chern-Simons theories, the Gaussian curvature prescription with conical singularities and Onsager's description of turbulence. We analyse the problem of existence variationally, and show how the angular distribution of the conformal volume near the singularities may lead to improvements in the Moser-Trudinger inequality, and in turn to lower bounds on the Euler-Lagrange functional. We then discuss existence and non-existence results.
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/05 - Analisi Matematica
English
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Bartolucci, D., Malchiodi, A. (2013). An Improved Geometric Inequality via Vanishing Moments, with Applications to Singular Liouville Equations. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 322(2), 415-452 [10.1007/s00220-013-1731-0].
Bartolucci, D; Malchiodi, A
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/89948
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