Estimates in Hölder Classes for the Solution of an Inhomogeneous Dirichlet Problem for a Singularly Perturbed Homogeneous Convection–Diffusion Equation

Abstract

An inhomogeneous Dirichlet boundary value problem for a singularly perturbed homogeneous convection–diffusion equation with constant coefficients is considered in a half-plane. Convection is assumed to be directed orthogonally to the half-plane boundary away from it. Assuming that the boundary function is from the space $${{C}^{{2,\lambda }}}$$ , $$0 < \lambda < 1$$ , an unimprovable estimate for the solution bounded at infinity is obtained in the appropriate Holder norm.