【摘 要】
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Let B1 be a unit disc of R2,and H be a completion of C0∞(B1) under the norm ||u||H2 =∫B1 (|▽u|2-u2/(1-|x|2)2) dx.Using blow-up analysis,Wang-Ye [1] proved ex
【机 构】
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Department of Mathematics, Renmin University of China, Beijing 100872, China
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Let B1 be a unit disc of R2,and H be a completion of C0∞(B1) under the norm ||u||H2 =∫B1 (|▽u|2-u2/(1-|x|2)2) dx.Using blow-up analysis,Wang-Ye [1] proved existence of extremals for a Hardy-Trudinger-Moser inequality.In particular,the supremumu∈H,sup||u||H≤∫B1e4πru2dx can be attained by some function u0 ∈ H with ||u0||H =1.This was improved by the author and Zhu [2] to a version involving the first eigenvalue of the Hardy-Laplacian operator-△-1/(1-|x|2)2.In this note,the results of [1,2] will be reproved by the method of energy estimate,which was recently developed by Malchiodi-Martinazzi [3] and Mancini-Martinazzi [4].
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