On the sharpness of Green's function estimates for a   convection-diffusion problem
  Linear singularly perturbed convection-diffusion problems with characteristic layers are considered in three dimensions. We demonstrate the sharpness of our recently obtained upper bounds for the associated Green's function and its derivatives in the $L_1$ norm. For this, in this paper we establish the corresponding lower bounds. Both upper and lower bounds explicitly show any dependence on the singular perturbation parameter. 
Sebastian Franz and Natalia Kopteva
math.NA math.AP