# 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}
}
• Published 1 July 2015
• Mathematics
• Communications in Partial Differential Equations
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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We show that the Moser-Trudinger inequality holds in a conformal disc if and only if the metric is bounded from above by the Hyperbolic metric. We also find a necessary and sufficient condition for
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The Moser-Trudinger embedding has been generalized by Adimurthi and Sandeep to the following weighted version: if $$\Omega \subset \mathbb {R}^2$$Ω⊂R2 is bounded, $$\alpha >0$$α>0 and $$\beta \in • Mathematics • 2007 Abstract.Let Ω be a bounded domain in$${\mathbb{R}}^{n}$$, we prove the singular Moser-Trudinger embedding:$$\mathop {\sup\limits_{\parallel u\parallel \leqslant 1\Omega } \int