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arXiv · 1508.02090

Singular Liouville Equations on $S^2$: Sharp Inequalities and Existence Results

Gabriele Mancini
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Abstract

We prove a sharp Onofri-type inequality and non-existence of extremals for a Moser-Tudinger functional on the sphere in the presence of potentials having positive order singularities. We also investigate the existence of critical points and give some sufficient conditions under symmetry or nondegeneracy assumptions.

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Gabriele Mancini. 2015-08-09. Singular Liouville Equations on $S^2$: Sharp Inequalities and Existence Results. https://arxiv.org/abs/1508.02090

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