Year: 2015
Author: Xiaobao Zhu
Journal of Partial Differential Equations, Vol. 28 (2015), Iss. 1 : pp. 39–46
Abstract
In this paper, we establish a singular Trudinger-Moser inequality for the whole hyperbolic space $$H^n: sup_{u∈W^{1,n}(H^n),∫_{H^n}|∇_H^nu|^ndμ ≤ 1}∫_{H^n}\frac{e^{α|u|\frac{n}{n-1}}-Σ^{n-2}_{k=0}\frac{α^k|u|^\frac{nk}{n-1}}{k!}}{ρ^β}dμ‹∞ ⇔ \frac{α}{α_n}+\frac{β}{n} ≤ 1,$$ where α>0,α ∈ [0,n), ρ and dμ are the distance function and volume element of $H^n$ respectively.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jpde.v28.n1.5
Journal of Partial Differential Equations, Vol. 28 (2015), Iss. 1 : pp. 39–46
Published online: 2015-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 8
Keywords: Singular Trudinger-Moser inequlity