The singular Moser- Trudger Inequality on simply connected domains
Analysis of PDEs
2016-01-25 v1
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.
Keywords
Cite
@article{arxiv.1507.00323,
title = {The singular Moser- Trudger Inequality on simply connected domains},
author = {Gyula Csato and Prosenjit Roy},
journal= {arXiv preprint arXiv:1507.00323},
year = {2016}
}