preprint

Inserted: 17 jul 2018

Year: 2018

Abstract:

We show a new example of blow-up behaviour for the prescribed $Q$-curvature equation in dimension $6$, namely given a sequence $(V_k)\subset C^0(\mathbb{R}^6)$ suitably converging we construct a sequence $(u_k)$ of radially symmetric solutions to the equation $$(-\Delta)³ u_k=Vk e^{6 u_k} \quad \text{in }\mathbb{R}^6,$$ with $u_k$ blowing up at the origin and on a sphere. We also prove sharp blow-up estimates.