【摘 要】
：
Let B be the unit disc in R2,(H) be the completion of C∞0(B) under the norm ‖u‖(H)=(∫B|▽u|2dx-∫Bu2/(1-|x|2)2dx)1/2,(∨)u∈C∞0(B).Using blow-up analysis,w
【机 构】
：
Department of Mathematics, Renmin University of China, Beijing 100872, China
论文部分内容阅读
Let B be the unit disc in R2,(H) be the completion of C∞0(B) under the norm ‖u‖(H)=(∫B|▽u|2dx-∫Bu2/(1-|x|2)2dx)1/2,(∨)u∈C∞0(B).Using blow-up analysis,we prove that for any γ ≤ 4π,the supremum supu∈(H),‖u‖1,h≤1∫Beγu2dx can be attained by some function u0 ∈ (H) with ‖u0‖1,h =1,where h is a decreasingly nonnegative,radially symmetric function,and satisfies a coercive condition.Namely there exists a constant δ ＞ 0 satisfying ‖u‖21,h=‖u‖2(H)-∫Bhu2dx≥δ‖u‖2(H),(∨)u∈(H).This extends earlier results of Wang-Ye [1] and Yang-Zhu [2].
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