Hölder estimates for the regular component of the solution to a singularly perturbed convection-diffusion equation

In a half-plane, a homogeneous Dirichlet boundary value problem for an inhomogeneous singularly perturbed convection-diffusion equation with constant coefficients and convection directed orthogonally away from the boundary of the half-plane is considered. Assuming that the right-hand side of the equation belongs to the space $C^\lambda$, $0<\lambda<1$, and the solution is bounded at infinity, an unimprovable estimate of the solution is obtained in a corresponding Hölder norm (anisotropic with respect to a small parameter).