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

作者：Hyder Ali; Iula Stefano; Martinazzi Luca

来源：Communications in Contemporary Mathematics, 2018, 20(2): 1750026.

DOI：10.1142/S0219199717500262

<jats:p>Let [Formula: see text] be an integer. For any open domain [Formula: see text], non-positive function [Formula: see text] such that [Formula: see text], and bounded sequence [Formula: see text] we prove the existence of a sequence of functions [Formula: see text] solving the Liouville equation of order [Formula: see text] [Formula: see text] and blowing up exactly on the set [Formula: see text], i.e. [Formula: see text] thus showing that a result of Adimurthi, Robert and Struwe is sharp. We extend this result to the boundary of [Formula: see text] and to the case [Formula: see text]. Several related problems remain open.</jats:p>

• 出版日期2018-3