Calculus of Variations and Geometric Measure Theory

A. Hyder - L. Martinazzi

Gluing metrics with prescribed $Q$-curvature and different asymptotic behaviour in dimension $6$

created by martinazz on 17 Jul 2018



Inserted: 17 jul 2018

Year: 2018

ArXiv: 1804.09261 PDF


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 $$(-\Delta)3 uk=Vk e{6 uk} \quad \text{in }\mathbb{R}6,$$ with $u_k$ blowing up at the origin and on a sphere. We also prove sharp blow-up estimates.