Singular Moser–Trudinger inequality on simply connected domains

@article{Csat2015SingularMI,
  title={Singular Moser–Trudinger inequality on simply connected domains},
  author={Gyula Csat{\'o} and Prosenjit Roy},
  journal={Communications in Partial Differential Equations},
  year={2015},
  volume={41},
  pages={838 - 847}
}
ABSTRACT In this paper the authors complete their study of the singularMoser-Trudinger embedding: in a previous result they have proven the existence of an extremal function for the singular Moser-Trudinger embedding where α > 0 and β ∈ [0, 2) are such that and Ω ⊂ ℝ2. This generalizes a well known result by Flucher, who has proven the case β = 0. This first proof is however far too technical and complicated for simply connected domains. Here we give a much simpler and more self-contained proof… 

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