文献类型：期刊文献

英文题名：An improved singular Trudinger-Moser inequality in unit ball

作者：Yuan, Anfeng[1,2];Zhu, Xiaobao[1]

第一作者：Yuan, Anfeng

通讯作者：Zhu, XB[1]

机构：[1]Renmin Univ China, Sch Informat, Dept Math, Beijing 100872, Peoples R China;[2]Beijing Union Univ, Dept Fdn Courses, Beijing 100101, Peoples R China

第一机构：Renmin Univ China, Sch Informat, Dept Math, Beijing 100872, Peoples R China

通讯机构：[1]corresponding author), Renmin Univ China, Sch Informat, Dept Math, Beijing 100872, Peoples R China.

年份：2016

卷号：435

期号：1

起止页码：244-252

外文期刊名：JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

收录：;Scopus(收录号：2-s2.0-84951162535);WOS:【SCI-EXPANDED(收录号:WOS:000365928200013)】；

基金：The authors thank Professor Yunyan Yang for his encouragements and many helpful discussions, thank the referee for his/her kindly suggestions. A. Yuan is supported by the Program of Beijing higher Education Youth Elite Teacher Project (YETP1776). X. Zhu is supported by the National Science Foundation of China, Grant Nos. 11171347, 41275063 and 1140575.

语种：英文

外文关键词：Trudinger-Moser inequality; Singular Trudinger-Moser inequality

摘要：Let B subset of R (n >= 2) be the unit ball centered at the origin with radius 1. Let beta, 0 <= beta < n, be fixed. Define lambda(beta)(B)= inf(u is an element of 01,n) (B) , u not equivalent to 0 integral(B) vertical bar del vertical bar(n)dx/integral(B) vertical bar x vertical bar(-beta) vertical bar u vertical bar(n)dx Suppose that gamma satisfies gamma/alpha(n) + beta/n = 1, where alpha(n) = n omega(1/(n-1))(n-1) is the area of the unit sphere in R-n. Using rearrangement argument, we prove that for any alpha, 0 <= alpha = lambda(beta) (B). This improves earlier results of Yang [15] and Adimurthi and Sandeep [2] in the unit ball. (C) 2015 Elsevier Inc. All rights reserved.