Local and global uniform convergence for elliptic problems on varying domains

摘要: Abstract The aim of the paper is to prove optimal results on local and global uniform convergence solutions elliptic equations with Dirichlet boundary conditions varying domains. We assume that limit domain be stable in sense Keldys [Amer. Math. Soc. Transl. 51 (1966) 1–73]. further approaching domains satisfy a necessary condition inside domain, only require L 2 -convergence outside. As consequence, are same trivial case homogenisation perforated domain. also able deal certain cracking