Hölder Estimates for the Regular Component of the Solution to a Singularly Perturbed Convection–Diffusion Equation

Abstract

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^λ, 0 < λ < 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).