Abstract
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).
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