Improved Moser-Trudinger Inequality Involving L p Norm in n Dimensions
Jiuyi Zhu · Advanced Nonlinear Studies · 2014
Abstract The paper is concerned about an improvement of Moser-Trudinger inequality involving L p 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 ω n−1 is the surface area of the unit ball in ℝ n . We also obtain the existence of the extremal functions for (0.2).