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 R x (-1, 1).
Remarks on the Moser-Trudinger inequality / Battaglia, Luca; Mancini, Gabriele. - In: ADVANCES IN NONLINEAR ANALYSIS. - ISSN 2191-9496. - 2:4(2013), pp. 389-425. [10.1515/anona-2013-0014]
Remarks on the Moser-Trudinger inequality
MANCINI, GABRIELE
2013
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 R x (-1, 1).File allegati a questo prodotto
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