Sobolev type embedding and weak solutions with a prescribed singular set

作     者：GUO ZongMing GUAN XiaoHong WAN FangShu 

作者机构：Department of Mathematics Henan Normal University 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2016年第59卷第10期

页      面：1975-1994页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：supported by National Natural Science Foundation of China (Grant Nos. 11171092 and 11571093) 

主　　题：positive weak solutions Sobolev type embeddings weighted elliptic equations prescribed singular sets 

摘      要：New Sobolev type embeddings for some weighted Banach spaces are established. Using such embeddings and the singular positive radial entire solutions, we construct singular positive weak solutions with a prescribed singular set for a weighted elliptic equation. Our main results in this paper also provide positive weak solutions with a prescribed singular set to an equation with Hardy potential.