Geodesic
Complete asymptotic expansions for eigenvalues of Dirichlet laplacian in thin three-dimensional rods
ESAIM: Control, Optimisation and Calculus of Variations, Tome 17 (2011) no. 3, pp. 887-908

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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 associated with these first eigenvalues.

DOI : 10.1051/cocv/2010028
Classification : 35P05, 35J05, 35B25, 35C20
Keywords: thin rod, Dirichlet laplacian, eigenvalue, asymptotics 
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     author = {Borisov, Denis and Cardone, Giuseppe},
     title = {Complete asymptotic expansions for eigenvalues of {Dirichlet} laplacian in thin three-dimensional rods},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {887--908},
     publisher = {EDP-Sciences},
     volume = {17},
     number = {3},
     year = {2011},
     doi = {10.1051/cocv/2010028},
     mrnumber = {2826984},
     zbl = {1223.35248},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2010028/}
}
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Borisov, Denis; Cardone, Giuseppe. Complete asymptotic expansions for eigenvalues of Dirichlet laplacian in thin three-dimensional rods. ESAIM: Control, Optimisation and Calculus of Variations, Tome 17 (2011) no. 3, pp. 887-908. doi: 10.1051/cocv/2010028

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