Complete asymptotic expansions for eigenvalues of Dirichlet Laplacian in thin three-dimensional rods
Denis Borisov, Giuseppe Cardone (2011)
ESAIM: Control, Optimisation and Calculus of Variations
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We consider the Dirichlet Laplacian in a thin curved three-dimensional rod. The rod is finite. Its cross-section is constant and small, and rotates along the reference curve in an arbitrary way. We find a two-parametric set of the eigenvalues of such operator and construct their complete asymptotic expansions. We show that this two-parametric set contains any prescribed number of the first eigenvalues of the considered operator. We obtain the complete asymptotic expansions for the eigenfunctions...