On Higher Integrability of Solutions to the Poisson Equation with Drift in Domains Perforated Along the Boundary
Gregory Aleksandrovich Chechkin, T. P. Chechkina · Russian Journal of Mathematical Physics · 2024
In the paper, we consider a linear second order elliptic problem with drift in a domain perforated along the boundary. Setting homogeneous Dirichlet condition on the boundary of the cavities and homogeneous Neumann condition on the outer boundary of the domain, we prove the higher integrability of the gradient of the solution to the problem (the Boyarsky–Meyers estimate). DOI 10.1134/S1061920824030051