Marcinkiewicz Estimates for Solutions of Some Elliptic Problems with Singular Data

In this paper we prove regularity result for solutions of the boundary value problem \( \left\{ \begin{array}{cl} -{{\,\textrm{div}\,}}(M(x)\,\nabla u) + u = -{{\,\textrm{div}\,}}(u\,E(x)) + f(x)\,, &{} \text{ in }\,\, \Omega , \\ u = 0\,, &{} \text{ on }\,\,\partial \Omega , \end{array} \right. \) $$\left\{\begin{array}{cc}-\text{div}(M(x)\mathrm{\nabla }u)+u=-\text{div}(uE(x))+f(x),& \text{in}\mathrm{\Omega },\hfill \\ u=0,& \text{on}\partial \mathrm{\Omega },\hfill \end{array}\right)$$ with the vector field E(x) and the function f(x) belonging to some Marcinkiewicz spaces.