Large blow-up sets for the prescribed Q-curvature equation in the Euclidean

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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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.
Faculties and Departments:05 Faculty of Science > Departement Mathematik und Informatik > Ehemalige Einheiten Mathematik & Informatik > Analysis (Martinazzi)
UniBasel Contributors:Martinazzi, Luca and Iula, Stefano and Hyder, Ali
Item Type:Article, refereed
Article Subtype:Research Article
Publisher:World Scientific Publishing
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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