Geodesic
Singularly perturbed Dirichlet boundary value problem for a stationary system in the linear elasticity theory
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2008), pp. 7-16

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We consider a singularly perturbed Dirichlet boundary value problem for an elliptic operator of the linear elasticity theory in a bounded domain with a small cavity. The main result is the proof of the theorem about the convergence of eigenelements of the perturbed boundary value problem to eigenelements of the corresponding limit boundary value problem, when the parameter $\varepsilon$ which defines the diameter of the small cavity tends to zero.
Keywords: operator, boundary value problem
Mots-clés : singular perturbation, eigenelements. 
@article{IVM_2008_12_a1,
     author = {D. B. Davletov},
     title = {Singularly perturbed {Dirichlet} boundary value problem for a stationary system in the linear elasticity theory},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {7--16},
     publisher = {mathdoc},
     number = {12},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2008_12_a1/}
}
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D. B. Davletov. Singularly perturbed Dirichlet boundary value problem for a stationary system in the linear elasticity theory. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2008), pp. 7-16. http://geodesic.mathdoc.fr/item/IVM_2008_12_a1/