Moser–Trudinger inequality involving the anisotropic Dirichlet norm (∫ΩFN(∇u)dx)1N on W01,N(Ω)

2019 ◽  
Vol 276 (9) ◽  
pp. 2901-2935 ◽  
Author(s):  
Changliang Zhou ◽  
Chunqin Zhou
Keyword(s):  
Dirichlet Norm ◽  
Trudinger Inequality

N-Laplacian Equations in ℝN with Subcritical and Critical GrowthWithout the Ambrosetti-Rabinowitz Condition

2013 ◽  
Vol 13 (2) ◽  
Author(s):  
Nguyen Lam ◽  
Guozhen Lu
Keyword(s):  
Bounded Domain ◽  
Exponential Growth ◽  
Nonnegative Solution ◽  
Nontrivial Solutions ◽  
Critical Exponential Growth ◽  
Trudinger Inequality ◽  
Laplacian Equations

AbstractLet Ω be a bounded domain in ℝwhen f is of subcritical or critical exponential growth. This nonlinearity is motivated by the Moser-Trudinger inequality. In fact, we will prove the existence of a nontrivial nonnegative solution to (0.1) without the Ambrosetti-Rabinowitz (AR) condition. Earlier works in the literature on the existence of nontrivial solutions to N−Laplacian in ℝ

Series expansion of Leray–Trudinger inequality

2021 ◽  
pp. 1-13
Author(s):  
Xiaomei Sun ◽  
Kaixiang Yu ◽  
Anqiang Zhu
Keyword(s):  
Series Expansion ◽  
Infinite Series ◽  
Hardy Inequality ◽  
Hardy’S Inequality ◽  
Optimal Form ◽  
Hardy's Inequality ◽  
Early Results ◽  
Trudinger Inequality

In this paper, we establish an infinite series expansion of Leray–Trudinger inequality, which is closely related with Hardy inequality and Moser Trudinger inequality. Our result extends early results obtained by Mallick and Tintarev [A. Mallick and C. Tintarev. An improved Leray-Trudinger inequality. Commun. Contemp. Math. 20 (2018), 17501034. OP 21] to the case with many logs. It should be pointed out that our result is about series expansion of Hardy inequality under the case $p=n$ , which case is not considered by Gkikas and Psaradakis in [K. T. Gkikas and G. Psaradakis. Optimal non-homogeneous improvements for the series expansion of Hardy's inequality. Commun. Contemp. Math. doi:10.1142/S0219199721500310]. However, we can't obtain the optimal form by our method.

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