A linear singularly perturbed convection-diffusion problem with characteristic layers is considered in three dimensions. Sharp bounds for the associated Green's function and its firstand
second-order derivatives are established in the L_1 norm by employing the parametrix metho'.
The dependence of these bounds on the small perturbation parameter is shown explicitly. The
obtained estimates will be used in a forthcoming numerical analysis of the considered problem to
derive a robust a posteriori error estimator in the maximum norm.