A Dirichlet problem involving the divergence operatord

We consider the problem {div u + (a; u) = f in Omega u = u(0) on partial derivative Omega. We show that if curl a (x(0)) not equal for some x(0) epsilon Omega, then the problem is solvable without restriction on f. We also discuss the regularity of the solution. (C) 2015 Elsevier Masson SAS. All rights reserved.