Scalar elliptic equations with a singular drift

Abstract

In this paper we prove the existence and uniqueness of weak solutions to the Dirichlet problem for an elliptic equation with a drift b satisfying div b ≤ 0 in Ω. We assume b belongs to some weak Morrey class which includes in the 3D case, in particular, drifts having a singularity along the axis x 3 with the asymptotic b(x) ∼ c/r, where r = x 2 1 + x 2 2 .