Calculus of Variations and Geometric Measure Theory
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G. Csato - P. Roy

The singular Moser- Trudger Inequality on simply connected domains

created by csato on 12 Nov 2021

[BibTeX]

preprint

Inserted: 12 nov 2021

Year: 2015

ArXiv: 1507.00323 PDF

Abstract:

In this paper the authors complete their study of the singular Moser-Trudinger embedding G. Csato and P. Roy, Extremal functions for the singular Moser-Trudinger inequality in 2 dimensions, Calc. Var. Partial Differential Equations, DOI 10.1007/s00526-015-0867-5, abbreviated CR. The proof in CR 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 CR more easily accessible.

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