1. Remarks on the Moser-Trudinger inequality
- Author
-
Luca Battaglia, Gabriele Mancini, Battaglia, Luca, and Mancini, Gabriele
- Subjects
Unit sphere ,Extremal ,Metrics ,Moser ,Strip ,Trudinger ,Unbounded ,Analysis ,QA299.6-433 ,Pure mathematics ,Inequality ,media_common.quotation_subject ,Mathematics::Analysis of PDEs ,Conformal map ,46E35, 26D10, 35A23, 58E35 ,Mathematics - Analysis of PDEs ,FOS: Mathematics ,Euclidean domain ,Metric ,Equivalence (measure theory) ,Mathematics ,Counterexample ,media_common ,Analysis of PDEs (math.AP) - Abstract
We extend the Moser-Trudinger inequality to any Euclidean domain satisfying Poincar\'e'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., Comment: 32 pages, accepted on Advances in Nonlinear Analysis
- Published
- 2013