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2014 Trudinger-Moser Embedding on the Hyperbolic Space
Yunyan Yang, Xiaobao Zhu
Abstr. Appl. Anal. 2014: 1-4 (2014). DOI: 10.1155/2014/908216


Let (n,g) be the hyperbolic space of dimension n. By our previous work (Theorem 2.3 of (Yang (2012))), for any 0<α<αn, there exists a constant τ>0 depending only on n and α such that supuW1,n(n),u1,τ1n(eαun/(n-1)-k=0n-2αk|u|nk/(n-1)/k!)dvg<, where αn=nωn-11/(n-1), ωn-1 is the measure of the unit sphere in n, and u1,τ=guLn(n)+τuLn(n). In this note we shall improve the above mentioned inequality. Particularly, we show that, for any 0<α<αn and any τ>0, the above mentioned inequality holds with the definition of u1,τ replaced by (n(|gu|n+τ|u|n)dvg)1/n. We solve this problem by gluing local uniform estimates.


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Yunyan Yang. Xiaobao Zhu. "Trudinger-Moser Embedding on the Hyperbolic Space." Abstr. Appl. Anal. 2014 1 - 4, 2014.


Published: 2014
First available in Project Euclid: 2 October 2014

zbMATH: 07023287
MathSciNet: MR3173294
Digital Object Identifier: 10.1155/2014/908216

Rights: Copyright © 2014 Hindawi

Vol.2014 • 2014
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