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Mathematics > Analysis of PDEs

arXiv:1804.09261 (math)
[Submitted on 24 Apr 2018 (v1), last revised 3 Jun 2019 (this version, v2)]

Title:Gluing metrics with prescribed $Q$-curvature and different asymptotic behaviour in high dimension

Authors:Ali Hyder, Luca Martinazzi
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Abstract:We show a new example of blow-up behaviour for the prescribed $Q$-curvature equation in even dimension $6$ and higher, namely given a sequence $(V_k)\subset C^0(\mathbb{R}^{2n})$ suitably converging we construct {for $n\geq 3$} a sequence $(u_k)$ of radially symmetric solutions to the equation $${(-\Delta)^n u_k=V_k e^{2n u_k} \quad \text{in }\mathbb{R}^{2n},}$$ with $u_k$ blowing up at the origin \emph{and} on a sphere. We also prove sharp blow-up estimates. This is in sharp contrast with the $4$-dimensional case studied by F. Robert (J. Diff. Eq. 2006).
Subjects: Analysis of PDEs (math.AP)
Cite as: arXiv:1804.09261 [math.AP]
  (or arXiv:1804.09261v2 [math.AP] for this version)
  https://doi.org/10.48550/arXiv.1804.09261

Submission history

From: Ali Hyder [view email]
[v1] Tue, 24 Apr 2018 21:20:30 UTC (110 KB)
[v2] Mon, 3 Jun 2019 20:02:25 UTC (111 KB)
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