Singular Moser–Trudinger inequality on simply connected domains
Gyula Csató, Prosenjit Roy · Communications in Partial Differential Equations · 2015
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 using complex analysis, which also generalizes the corresponding proof given by Flucher for such domains. This should make the previous work by the authors more easily accessible.