【摘 要】
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Let Ω (∈) R2 be a smooth bounded domain with 0 ∈ (e)Ω.In this paper,we prove that for any β ∈ (0,1),the supremum dx u∈W1,2(Ω),∫Ω supudx=0,∫Ω |▽u|2dx≤1 ∫Ω e2π(1-β)u2/|x|2β is finite and can be attained.This partially generalizes a well-known work of Chang
【机 构】
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School of Mathematics,Renmin University of China,Beijing 100872,China
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Let Ω (∈) R2 be a smooth bounded domain with 0 ∈ (e)Ω.In this paper,we prove that for any β ∈ (0,1),the supremum dx u∈W1,2(Ω),∫Ω supudx=0,∫Ω |▽u|2dx≤1 ∫Ω e2π(1-β)u2/|x|2β is finite and can be attained.This partially generalizes a well-known work of Chang and Yang (1988) who have obtained the inequality when β =0.
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