Nonexistence of extremals for an inequality of Adimurthi-Druet on a closed Riemann surface

• 作者: Yunyan Yang
• 来源期刊: 中国科学：数学（英文版）
• 年，卷（期）: 2020,（8）
• 所属期刊栏目: Articles
• 页码范围: 1627-1644
• 页数: 18页
• 语种: 英文

摘要

Based on a recent work of Mancini and Thizy (2019),we obtain the nonexistence of extremals for an inequality of Adimurthi and Druet (2004) on a closed Riemann surface (∑,g).Precisely,if λ1 (∑) is the first eigenvalue of the Laplace-Beltrami operator with respect to the zero mean value condition,then there exists a positive real number α* ＜ λ1(∑) such that for all α ∈ (α*,λ1(∑)),the supremum u∈W1,2(∑,g),f∑sup udvg=0,‖▽gu‖2≤1∫∑exp(4πu2(1 + α‖u‖22))dvgcannot be attained by any u ∈ W1,2(∑,g) with f∑ udvg =0 and ‖▽gu‖2 ≤ 1,where W1,2(∑,g) denotes the usual Sobolev space and ‖· ‖2 =(∫∑ |· |2dvg)1/2 denotes the L2(∑,g)-norm.This complements our earlier result in Yang (2007).

作者信息

序号	姓名	单位	发文数	被引次数	H指数	G指数
1	Yunyan Yang		1	0	0.0	0.0