Abstract
The paper is concerned about an improvement of Moser-Trudinger inequality involving Lp norm for a bounded domain in n dimensions. Let
be the first eigenvalue associated with n-Laplacian. We obtain the following strengthened Moser-Trudinger inequality with blow-up analysis
for 0 ≤ α < λ̅(Ω) and 1 < p ≤ n, and the supremum is infinity for α ≥ λ̅(Ω), where 
and ωn−1 is the surface area of the unit ball in ℝn. We also obtain the existence of the extremal functions for (0.2).
Published Online: 2016-03-10
Published in Print: 2014-05-01
© 2016 by Advanced Nonlinear Studies, Inc.
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
