Martinazzi, Luca.
(2011)
* Quantization for the prescribed Q-curvature equation on open domains.*
Communications in Contemporary Mathematics, 13.
pp. 533-551.

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Official URL: http://edoc.unibas.ch/49902/

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## Abstract

We discuss compactness, blow-up and quantization phenomena for the prescribed Q-curvature equation (−Δ)muk=Vke2muk on open domains of $\R{2m}$. Under natural integral assumptions we show that when blow-up occurs, up to a subsequence

limk→∞∫Ω0Vke2mukdx=LΛ1,

where Ω0⊂⊂Ω is open and contains the blow-up points, L∈N and $\Lambda_1:=(2m-1)!\vol(S^{2m})$ is the total Q-curvature of the round sphere S2m. Moreover, under suitable assumptions, the blow-up points are isolated. We do not assume that V is positive.

limk→∞∫Ω0Vke2mukdx=LΛ1,

where Ω0⊂⊂Ω is open and contains the blow-up points, L∈N and $\Lambda_1:=(2m-1)!\vol(S^{2m})$ is the total Q-curvature of the round sphere S2m. Moreover, under suitable assumptions, the blow-up points are isolated. We do not assume that V is positive.

Faculties and Departments: | 05 Faculty of Science > Departement Mathematik und Informatik > Mathematik |
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UniBasel Contributors: | Martinazzi, Luca |

Item Type: | Article, refereed |

Article Subtype: | Research Article |

Publisher: | World Scientific Publishing |

ISSN: | 0219-1997 |

e-ISSN: | 1793-6683 |

Note: | Publication type according to Uni Basel Research Database: Journal article |

Identification Number: | |

Last Modified: | 17 Jan 2018 10:07 |

Deposited On: | 17 Jan 2018 10:07 |

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