TY - JOUR
T1 - A Singular Trudinger-Moser Inequality in Hyperbolic Space
AU - Zhu , Xiaobao
JO - Journal of Partial Differential Equations
VL - 1
SP - 39
EP - 46
PY - 2015
DA - 2015/03
SN - 28
DO - http://doi.org/10.4208/jpde.v28.n1.5
UR - https://global-sci.org/intro/article_detail/jpde/5101.html
KW - Singular Trudinger-Moser inequlity
KW - hyperbolic space
AB -  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.