On the Boyarsky-Meyers estimates

In the talk one can find some results on higher integrability of gradients of solution to linear and nonlinear elliptic equations with changing type of boundary conditions (neumann and Dirichlet). Given the capacity of the part of the boundary with Dirichlet data, we prove higher integrability of solutions (the Boyarsky-Meyers estimates).
The results are the joint work with Yu. A. Alkhutov, T.P. Chechkina, and V.G. Maz'ya.