In an unbounded domain of \(\mathbb {R}^N\) , \(N \ge 2\) , we prove existence and Stampacchia type regularity of solutions to some noncoercive nonlinear Dirichlet problems whose model case appears in stationary convection–diffusion phenomena. The drift term is controlled through a function in a suitable functional space, strictly containing Lebesgue one. We obtain some a priori estimates, by contradiction, via a weak maximum principle.
