On the Boyarsky–Meyers Estimate for the Gradient of the Solution to the Dirichlet Problem for a Second-Order Linear Elliptic Equation with Drift: The Case of Critical Sobolev Exponent

Abstract

Increased integrability of the gradient of the solution to the homogeneous Dirichlet problem for the Poisson equation with lower terms in a bounded Lipschitz domain is established. The unique solvability of this problem is also proved.