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Volume 28, Issue 1
A Singular Trudinger-Moser Inequality in Hyperbolic Space

Xiaobao Zhu

DOI: 10.4208/jpde.v28.n1.5

J. Part. Diff. Eq., 28 (2015), pp. 39-46.

Published online: 2015-03

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  • 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.
  • Keywords

Singular Trudinger-Moser inequlity hyperbolic space

  • AMS Subject Headings

58E35, 35B33, 35J20, 35J60

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

zhuxiaobao@ruc.edu.cn (Xiaobao Zhu)

  • BibTex
  • RIS
  • TXT
@Article{JPDE-28-39, author = {Zhu , Xiaobao}, title = {A Singular Trudinger-Moser Inequality in Hyperbolic Space}, journal = {Journal of Partial Differential Equations}, year = {2015}, volume = {28}, number = {1}, pages = {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.}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v28.n1.5}, url = {http://global-sci.org/intro/article_detail/jpde/5101.html} }
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.
Zhu , Xiaobao. (2015). A Singular Trudinger-Moser Inequality in Hyperbolic Space. Journal of Partial Differential Equations. 28 (1). 39-46. doi:10.4208/jpde.v28.n1.5
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