We extend the Moser-Trudinger inequality (Equation Presented) to any Euclidean domain satisfying Poincaré's inequality (Equation Presented) 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 Ω: = ℝ x (-1, 1).

Remarks on the Moser-Trudinger inequality

Mancini G.
2013-01-01

Abstract

We extend the Moser-Trudinger inequality (Equation Presented) to any Euclidean domain satisfying Poincaré's inequality (Equation Presented) 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 Ω: = ℝ x (-1, 1).
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11586/385896
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 18
  • ???jsp.display-item.citation.isi??? 17
social impact