Embeddings of weighted Sobolev spaces and degenerate elliptic problems  

作　　者：GUO ZongMing MEI LinFeng WAN FangShu GUAN XiaoHong 

机构地区：[1]Department of Mathematics, Henan Normal University

出　　处：《Science China Mathematics》2017年第8期1399-1418,共20页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China (Grant Nos. 11171092, 11571093 and 11371117)

摘　　要：New embeddings of some weighted Sobolev spaces with weights a(x)and b(x)are established.The weights a(x)and b(x)can be singular.Some applications of these embeddings to a class of degenerate elliptic problems of the form-div(a(x)?u)=b(x)f(x,u)in?,u=0 on??,where?is a bounded or unbounded domain in RN,N 2,are presented.The main results of this paper also give some generalizations of the well-known Caffarelli-Kohn-Nirenberg inequality.New embeddings of some weighted Sobolev spaces with weights a（x）and b（x）are established.The weights a（x）and b（x）can be singular.Some applications of these embeddings to a class of degenerate elliptic problems of the form-div（a（x）？u）=b（x）f（x,u）in？,u=0 on？？,where？is a bounded or unbounded domain in RN,N 2,are presented.The main results of this paper also give some generalizations of the well-known Caffarelli-Kohn-Nirenberg inequality.

关 键 词：positive weak solutions Sobolev type embeddings weighted elliptic equations Caffarelli-Kohn- Nirenberg inequality 

分 类 号：O175.25[理学—数学]