Large blow-up sets for the prescribed Q-curvature equation in the Euclidean space
Copyright policy )Large blow-up sets for the prescribed Q-curvature equation in the Euclidean space
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.
- University of Basel Switzerland
- University of Padua Italy
- Sapienza University of Rome Italy
Blow-up in context of PDEs, Mathematics - Analysis of PDEs, blow-up; conformal geometry; Liouville equation; Q -curvature; mathematics (all); applied mathematics, Liouville equation of order \(2m\), FOS: Mathematics, blow-up; conformal geometry; Liouville equation; Q -curvature; Mathematics (all); Applied Mathematics, Higher-order elliptic equations, blow-up, Analysis of PDEs (math.AP)
Blow-up in context of PDEs, Mathematics - Analysis of PDEs, blow-up; conformal geometry; Liouville equation; Q -curvature; mathematics (all); applied mathematics, Liouville equation of order \(2m\), FOS: Mathematics, blow-up; conformal geometry; Liouville equation; Q -curvature; Mathematics (all); Applied Mathematics, Higher-order elliptic equations, blow-up, Analysis of PDEs (math.AP)
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