In this paper, the author studies the Poisson equation when the forcing term is the divergence of a vector field whose entries exhibit singularities. The author formulates this problem in a Sobolev power weighted space, and applies a generalization of the Lax-Milgram theorem to establish the well-posedness of the Neumann boundary value problem.

The proof of the main theorem relies on delicate estimates and, to be appreciated, requires a strong background in the analysis of elliptic boundary value problems. Although the technical treatments are organized well, the paper is not written very well. In particular, very little attempt is made to show why the subject matter is significant, and most important, why the analysis presented is relevant to simulation.