A singular Moser-Trudinger inequality for mean value zero functions in dimension two

• 作者: Xiaobao Zhu
• 来源期刊: 中国科学：数学（英文版）
• 年，卷（期）: 2021,（11）
• 所属期刊栏目: Articles
• 页码范围: 2521-2538
• 页数: 18页
• 语种: 英文

摘要

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.