Pointwise estimate of a solution to quasilinear elliptic problem in the domain with thin cavity

• Date: 1992
• Main Authors: Skrypnik, I. V., Naumova, M. A., Скрыпник, И. В., Наумова, М. А.
• Format: Article
• Language: Russian
• Published: Institute of Mathematics, NAS of Ukraine 1992
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/8241
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We derive a pointwise estimate of the solution to Dirichlet’s problem for a quasilinear second–order elliptic equation in a domain whose bounded compliment is contained in a small neighborhood of a set $\{x\in R^n: |x|\leq ½,x_1=\dots=x_s=0\}$.