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We derive asymptotic formulas for the solutions of the mixed boundary valueproblem for the Poisson equation on the union of a thin cylindrical plate andseveral thin cylindrical rods. One of the ends of each rod is set into a holein the plate and the other one is supplied with the Dirichlet condition. TheNeumann conditions are imposed on the whole remaining part of the boundary.Elements of the junction are assumed to have contrasting properties so that thesmall parameter, i.e. the relative thickness, appears in the differentialequation, too, while the asymptotic structures crucially depend on thecontrastness ratio. Asymptotic error estimates are derived in anisotropicweighted Sobolev norms.

Scalar boundary value problems on junctions of thin rods and plates. I. Asymptotic analysis and error estimates