# 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…

## 27 Citations

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