Positive solutions of critical semilinear elliptic equations on non-contractible planar domains

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A sharp form of the Moser-Trudinger inequality on a compact Riemannian surface (2007, background): “We need a result of Brezis and Merle [2]: Modifying the argument of Struwe [16], we have the following: Then for any 1 q 2 , (cid:3)∇ u (cid”
Critical points of the Moser-Trudinger functional on a disk (2012, result): “We also refer to [27] and [16] for related results on domains with small holes, in the spirit of [8] (where the Yamabe equation was treated).”
New solutions for Trudinger–Moser critical equations in R2 (2010, background): “Struwe in [21] built in the case of a domain with a sufficiently small hole (in the sense of Bahri and Coron [6,10]) a solution taking advantage of the presence of topology.”