We derive asymptotic formulas for the solutions of the mixed boundary value problem forthe Poisson equation on the union of a thin cylindrical plate and several thin cylindricalrods. One of the ends of each rod is set into a hole in the plate and the other one issupplied with the Dirichlet condition. The Neumann conditions are imposed on the wholeremaining part of the boundary. Elements of the junction are assumed to have contrastingproperties so that the small parameter, i.e. the relative thickness,appears in the differential equation, too, while the asymptotic structures cruciallydepend on the contrastness ratio. Asymptotic error estimates are derived in anisotropicweighted Sobolev norms.
