We study the metrics of constant Q-curvature in the Euclidean space with a prescribed singularity at the origin, namely solutions to a singular Liouville equation under a finite volume condition. We analyze the asymptotic behavior at infinity and the existence of solutions for every n larger than 3 also in a supercritical regime. Finally, we state some open problems.
Local and Nonlocal Singular Liouville Equations in Euclidean Spaces
MANCINI, GABRIELE;
2021-01-01
Abstract
We study the metrics of constant Q-curvature in the Euclidean space with a prescribed singularity at the origin, namely solutions to a singular Liouville equation under a finite volume condition. We analyze the asymptotic behavior at infinity and the existence of solutions for every n larger than 3 also in a supercritical regime. Finally, we state some open problems.File in questo prodotto:
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2 - Local and nonlocal singular Liouville equations in Euclidean spaces.pdf
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classification sing - revised.pdf
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