In this paper we prove a decomposition formula of Grisvard type, but for mixed boundary value problems of Dirichlet-oblique derivative type for general elliptic equations of second order in a plane domain with piecewise differentiable boundary. The main result extends previous results in this area by showing that, if the problem is posed in the Sobolev space H²(Ω), then a decomposition of the solution into a regular and an explicitly determined singular part holds for all combinations of the measure of the angle at the corner and the type of boundary conditions imposed in its neighbourhood.