加权Sobolev空间中的Poincaré不等式

基金项目: 国家自然科学基金资助项目(10261004,10461006);高校重点实验室访问学者基金;内蒙古自治区自然科学基金资助项目(200408020104)

Poincaré Inequalities in Weighted Sobolev Spaces

1.
Deptartment of Mathematics, Inner Mongolia University, Huhhot 010021, P. R. China;

摘要: 在加权Sobolov空间中讨论了加权的Poincaré不等式,利用嵌入映射给出了加权Poincaré不等式成立的充分和必要条件．
- 加权的Sobolev空间 /
- Poincaré不等式 /
- 嵌入映射
Abstract: The weighted Poincar inequalities in weighted Sobolev spaces were discussed and some necessary and sufficient conditions for them to hold were given.
- weighted Sobolev spaces /
- Poincar inequality /
- embedding

[1]	Amick C J.Some remarks on Rellich's theorem and the Poincare inequality[J].J London Mathematics Society,1978,18(2):319—328.
[2]	Edmunds D E,Evans W D.Spectral Theory and embeddings of Sobolev spaces[J].Quarterly J Mathematics Oxford Series,1979,30(2):431—453. doi: 10.1093/qmath/30.4.431
[3]	Edmunds D E,Evans W D.Spectral Theory and Differential Operators[M].Oxford:Oxford University Press,1987,1—50.
[4]	Hurri R.The weighted Poincare inequalities[J].Mathematics Scand,1990,67(1):145—160.
[5]	Kufner A.Weighted Sobolev Spaces[M].Wiley:Wiley Chichester Press,1985，1—100.
[6]	Kufner A,Opic B.How to define reasonably weighted Sobolev spaces[J].Commentarii Mathematics University Coarlinae,1984，25(3):537—554.
[7]	Edmunds D E,Opic B.Weighted Poincaré and friedrichs inequalitics[J].J London Mathematics Society,1993,47(2):79—96. doi: 10.1112/jlms/s2-47.1.79
[8]	Edmunds D E,Opic B,Pick L.Poincaré and friedrichs inequalities in abstract Sobolev spaces[J].Mathematics Proceeding Cambridge Philosophy Society,1993,113(1):355—379. doi: 10.1017/S0305004100076027
[9]	Edmunds D E,Opic B，Rakosnik J.Poincare and Friedrichs inequalities in abstract Sobolev spaces(2)[J].Mathematics Proceeding Cambridge Philosophy Society,1994,115(1):159—173. doi: 10.1017/S0305004100071991