Singular Moser–Trudinger inequality on simply connected domains. Issue 5 (3rd May 2016)

• Record Type: Journal Article
• Authors: Csató, Gyula; Roy, Prosenjit
• Is Part Of: Communications in partial differential equations. Volume 41:Issue 5(2016)
• Page Start: 838
• Page End: 847
• Publication Date: 2016-05-03
• Subjects: Concentration -- extremal function -- Moser-Trudinger embedding -- singular weight; Primary: 35B38; Differential equations, Partial -- Periodicals; 515.353
• DOI: 10.1080/03605302.2015.1123276
• Languages: English
• ISSNs: 0360-5302

Abstract

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 ⊂ ℝ 2 . 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.