Remarks on the Moser-Trudinger inequality
Analysis of PDEs
2020-06-16 v2
Abstract
We extend the Moser-Trudinger inequality to any Euclidean domain satisfying Poincar\'e's inequality. We find out that the same equivalence does not hold in general for conformal metrics on the unit ball, showing counterexamples. We also study the existence of extremals for the Moser-Trudinger inequalities for unbounded domains, proving it for the infinite planar strip.
Keywords
Cite
@article{arxiv.1307.0746,
title = {Remarks on the Moser-Trudinger inequality},
author = {Luca Battaglia and Gabriele Mancini},
journal= {arXiv preprint arXiv:1307.0746},
year = {2020}
}
Comments
32 pages, accepted on Advances in Nonlinear Analysis