The Meyers Estimates for Domains Perforated along the Boundary

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.

Automated summary

This paper considers an elliptic problem in a domain perforated along the boundary. By imposing certain boundary conditions, the higher integrability of the gradient of the solution is proven.