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arXiv · 1808.03624

Local and nonlocal singular Liouville equations in Euclidean spaces

Ali Hyder·Gabriele Mancini·Luca Martinazzi
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Abstract

We study metrics of constant $Q$-curvature in the Euclidean space with a prescribed singularity at the origin, namely solutions to the equation $$(-\Delta)^\frac{n}{2}w=e^{nw}-c\delta_{0} \text{ on } \mathbb R^n,$$ under a finite volume condition. We analyze the asymptotic behaviour at infinity and the existence of solutions for every $n\ge 3$ also in a supercritical regime. Finally, we state some open problems.

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Ali Hyder, Gabriele Mancini, Luca Martinazzi. 2018-08-10. Local and nonlocal singular Liouville equations in Euclidean spaces. https://arxiv.org/abs/1808.03624

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