Hyder, Ali and Iula, Stefano and Martinazzi, Luca.
(2018)
* Large blow-up sets for the prescribed Q-curvature equation in the Euclidean.*
Communications in Contemporary Mathematics, 20 (2).
p. 1750026.

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Official URL: https://edoc.unibas.ch/59717/

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## Abstract

Let m≥2 be an integer. For any open domain Ω⊂R2m, non-positive function φ∈C∞(Ω) such that Δmφ≡0, and bounded sequence (Vk)⊂L∞(Ω) we prove the existence of a sequence of functions (uk)⊂C2m−1(Ω) solving the Liouville equation of order 2m (−Δ)muk=Vke2mukin Ω,limsupk→∞∫Ωe2mukdx<∞,

and blowing up exactly on the set Sφ:={x∈Ω:φ(x)=0}, i.e.

limk→∞uk(x)=+∞ for x∈Sφandlimk→∞uk(x)=−∞ for x∈Ω∖Sφ,

thus showing that a result of Adimurthi, Robert and Struwe is sharp. We extend this result to the boundary of Ω and to the case Ω=R2m. Several related problems remain open.

and blowing up exactly on the set Sφ:={x∈Ω:φ(x)=0}, i.e.

limk→∞uk(x)=+∞ for x∈Sφandlimk→∞uk(x)=−∞ for x∈Ω∖Sφ,

thus showing that a result of Adimurthi, Robert and Struwe is sharp. We extend this result to the boundary of Ω and to the case Ω=R2m. Several related problems remain open.

Faculties and Departments: | 05 Faculty of Science > Departement Mathematik und Informatik > Ehemalige Einheiten Mathematik & Informatik > Analysis (Martinazzi) |
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UniBasel Contributors: | Martinazzi, Luca and Iula, Stefano and Hyder, Ali |

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: | 09 Sep 2020 08:38 |

Deposited On: | 09 Sep 2020 08:38 |

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