We extend the Moser–Trudinger inequality
to any Euclidean domain satisfying Poincaré'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 .
© 2013 by Walter de Gruyter Berlin Boston
This article is distributed under the terms of the Creative Commons Attribution Non-Commercial License, which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.