Abstract.
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 
.
Received: 2013-07-06
Accepted: 2013-09-26
Published Online: 2013-10-08
Published in Print: 2013-11-01
© 2013 by Walter de Gruyter Berlin Boston
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