On the Bojarskii–Meyers estimates

In the talk, we consider boundary value problems for second-order elliptic equations in domains with micro-inhomogeneities depending on a small parameter, in the vicinity of the boundary. For the solutions of these problems, it has been proved the higher integrability of the gradient of the solution. Such inequalities will be used for a priori estimates of solutions and for estimations of the rate of convergence as a small parameter tends to zero.