The Meyers Estimates for Domains Perforated along the Boundary
Г. А. Чечкин
Abstract
In this paper, we consider an elliptic problem in a domain perforated along the boundary. By setting a homogeneous Dirichlet condition on the boundary of the cavities and a homogeneous Neumann condition on the outer boundary of the domain, we prove higher integrability of the gradient of the solution to the problem.
Topics & Concepts
HomogeneousNeumann boundary conditionBoundary (topology)Boundary value problemDomain (mathematical analysis)Dirichlet boundary conditionMathematical analysisMixed boundary conditionMathematicsCombinatoricsAdvanced Mathematical Modeling in EngineeringNonlinear Partial Differential EquationsAnalytic and geometric function theory