Trudinger‐Moser Embedding on the Hyperbolic Space

Yunyan Yang and Xiaobao Zhu

Abstract and Applied Analysis, 2014, vol. 2014, issue 1

Abstract: Let (ℍn, g) be the hyperbolic space of dimension n. By our previous work (Theorem 2.3 of (Yang (2012))), for any 0 0 depending only on n and α such that supu∈W1,n(ℍn),∥u∥1,τ≤1∫ℍn (eαun/(n-1)-∑k=0n-2αk|u|nk/(n-1)/k!)dvg 0, the above mentioned inequality holds with the definition of ∥u∥1,τ replaced by (∫ℍn (|∇gu|n+τ|u|n)dvg) 1/n. We solve this problem by gluing local uniform estimates.

Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:908216

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