Martinazzi, Luca and Struwe, Michael.
(2012)
* Quantization for an elliptic equation of order 2m with critical exponential non-linearity.*
Mathematische Zeitschrift, 270 (1-2).
pp. 453-487.

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Official URL: http://edoc.unibas.ch/49900/

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## Abstract

On a smoothly bounded domain \({\Omega\subset\mathbb{R}^{2m}}\) we consider a sequence of positive solutions \({u_k\stackrel{w}{\rightharpoondown}0}\) in H m (Ω) to the equation \({(-\Delta)^m u_k=\lambda_k u_k e^{mu_k^2}}\) subject to Dirichlet boundary conditions, where 0 < λ k → 0. Assuming that

$$0 < \Lambda:=\lim_{k\to\infty}\int\limits_\Omega u_k(-\Delta)^m u_k dx < \infty,$$

we prove that Λ is an integer multiple of Λ1 := (2m − 1)! vol(S 2m ), the total Q-curvature of the standard 2m-dimensional sphere.

$$0 < \Lambda:=\lim_{k\to\infty}\int\limits_\Omega u_k(-\Delta)^m u_k dx < \infty,$$

we prove that Λ is an integer multiple of Λ1 := (2m − 1)! vol(S 2m ), the total Q-curvature of the standard 2m-dimensional sphere.

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: | Springer |

ISSN: | 0025-5874 |

e-ISSN: | 1432-1823 |

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

Identification Number: | |

Last Modified: | 22 Jan 2018 10:27 |

Deposited On: | 22 Jan 2018 10:27 |

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