We study the metrics of constant Q-curvature in the Euclidean space with a prescribed singularity at the origin, namely solutions to the equation −Deltaw = e^(nw) − c δ_0 on R^n, under a finite volume condition. We analyze the asymptotic behavior at infinity and the existence of solutions for every n ≥ 3 also in a supercritical regime. Finally, we state some open problems.
Local and nonlocal singular Liouville equations in Euclidean spaces / Hyder, Ali; Mancini, Gabriele; Martinazzi, Luca. - In: INTERNATIONAL MATHEMATICS RESEARCH NOTICES. - ISSN 1073-7928. - 2021:15(2021), pp. 11393-11425. [10.1093/imrn/rnz149]
Local and nonlocal singular Liouville equations in Euclidean spaces
Mancini, Gabriele;Martinazzi, Luca
2021
Abstract
We study the metrics of constant Q-curvature in the Euclidean space with a prescribed singularity at the origin, namely solutions to the equation −Deltaw = e^(nw) − c δ_0 on R^n, under a finite volume condition. We analyze the asymptotic behavior at infinity and the existence of solutions for every n ≥ 3 also in a supercritical regime. Finally, we state some open problems.| File | Dimensione | Formato | |
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