Abstract: We consider a 3d multi-structure composed of two joined perpendicular thin films: a vertical one with small thickness hna and a horizontal one with small thickness hnb. We study the asymptotic behavior, as hna and hnb tend to zero, of an eigenvalue problem for the Laplacian defined on this multi-structure. We shall prove that the limit problem depends on the value q=limnhnbhna. Precisely, we pinpoint three different limit regimes according to q belonging to] 0 , + ?[, q equal to + ?, or q equal to 0. We identify the limit problems and we also obtain H1-strong convergence results.

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