Embeddings of weighted Sobolev spaces and degenerate elliptic problems

• 来源期刊: 中国科学：数学（英文版）
• 年，卷（期）: 2017,（8）
• 页码范围: 1399-1418
• 页数: 20页
• 语种: 英文
• DOI: 10.1007/s11425-016-0403-6

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 Ω,u =0 on (a)Ω,where Ω 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.