On Compensated Compactness for Nonlinear Elliptic Problems in Perforated Domains
We consider a sequence of Dirichlet problems for a nonlinear divergent operator A: W m 1(Ω s ) → [W m 1(Ω s )]* in a sequence of perforated domains Ω s ⊂ Ω. Under a certain condition imposed on the local capacity of the set Ω \ Ω s , we prove the following principle of compensated compactness:...
Saved in:
| Date: | 2000 |
|---|---|
| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Institute of Mathematics, NAS of Ukraine
2000
|
| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/4559 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
| Download file: |  |
Institution
Ukrains’kyi Matematychnyi Zhurnal| Summary: | We consider a sequence of Dirichlet problems for a nonlinear divergent operator A: W m 1(Ω s ) → [W m 1(Ω s )]* in a sequence of perforated domains Ω s ⊂ Ω. Under a certain condition imposed on the local capacity of the set Ω \ Ω s , we prove the following principle of compensated compactness: \({\mathop {\lim }\limits_{s \to \infty }} \left\langle {Ar_s ,z_s } \right\rangle = 0\) , where r s(x) and z s(x) are sequences weakly convergent in W m 1(Ω) and such that r s(x) is an analog of a corrector for a homogenization problem and z s(x) is an arbitrary sequence from \({\mathop {W_m^1 }\limits^ \circ} (\Omega _s)\) whose weak limit is equal to zero. |
|---|