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 (Vk ) ⇢ C0(R2n) suitably converging we construct for n 3 a sequence (uk ) of radially symmetric solutions to the equation (1) nuk = Vk e2nuk in R2n, with uk blowing up at the origin and on a sphere. We also prove sharp blowup estimates. This is in sharp contrast with the 4-dimensional case studied by F. Robert (J. Differential Equation, 2006).
Gluing metrics with prescribed $Q$-curvature and different asymptotic behaviour in high dimension / Hyder, Ali; Martinazzi, Luca Massimo Andrea. - In: ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA. CLASSE DI SCIENZE. - ISSN 0391-173X. - XXII:2(2020), pp. 505-547. [10.2422/2036-2145.201905_001]
Gluing metrics with prescribed $Q$-curvature and different asymptotic behaviour in high dimension
Martinazzi, Luca Massimo Andrea
2020
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 (Vk ) ⇢ C0(R2n) suitably converging we construct for n 3 a sequence (uk ) of radially symmetric solutions to the equation (1) nuk = Vk e2nuk in R2n, with uk blowing up at the origin and on a sphere. We also prove sharp blowup estimates. This is in sharp contrast with the 4-dimensional case studied by F. Robert (J. Differential Equation, 2006).| File | Dimensione | Formato | |
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