Remarks on the Moser-Trudinger inequality

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.

32 pages, accepted on Advances in Nonlinear Analysis

References in corpus (1)

• Remarks on the Moser-Trudinger inequality

Cited by in corpus (5)

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• Adams Inequality on Pinched Hadamard Manifolds