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Quantization for an elliptic equation of order 2m with critical exponential non-linearity

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.
Faculties and Departments:05 Faculty of Science > Departement Mathematik und Informatik > Mathematik
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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