On Compensated Compactness for Nonlinear Elliptic Problems in Perforated Domains

• Date: 2000
• Main Authors: Skrypnik, I. V., Скрипник, І. В.
• 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
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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:...