By Esposito P., Grossi M., Pistoia A.
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Extra info for On the existence of blowing-up solutions for a mean field equation
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15) follows. 6. , k. If p ≥ 1 and i = h, then ρ2 eUi P ψhj Lp =O ρ 2(1−p) p as ρ → 0. Proof We have |eUi P ψhj |p = ρ2p ρ2p Ω |eUi P ψhj |p . 4 we get |eUi P ψhj |p = O(ρp ). 24) we obtain the desired estimate. 33 p Lp = O(ρ2−2p ). 7. Let j = 1, 2 and i = 1, . . , k. If p ≥ 1, then ρ2 eUi (P ψij − ψij ) Lp = O ρ2 1−p p as ρ → 0. 2 we get, ρ2 eUi (P ψij − ψij ) 10 Lp =O ρ2 eUi Lp = O(ρ2 1−p p ). Appendix D We are interested to prove a result concerning the structure of the solutions of the linearized problem “at infinity”.
J. Math. 25 (1995), 957-975.  W. Ding, J. Jost, J. Li, G. Wang, Existence results for mean field equations, Ann. IHP Analyse Non Lin´eaire 16 (1999), 653-666.  K. El Mehdi, M. Grossi, Asymptotic estimates and qualitative properties of an elliptic problem in dimension two, preprint. 36  P. Esposito, Blow up solutions for a Liouville equation with singular data, preprint (2003).  P. Esposito, A class of Liouville-type equations arising in Chern-Simons vortex theory: asymptotics and construction of blowing up solutions, Thesis, Roma “Tor Vergata” (2003).