Geodesic
On the resolvent of multidimensional operators with frequently changing boundary conditions in the case of the homogenized Dirichlet condition
Sbornik. Mathematics, Tome 205 (2014) no. 10, pp. 1492-1527

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We consider an elliptic operator in a multidimensional domain with frequently changing boundary conditions in the case when the homogenized operator contains the Dirichlet boundary condition. We prove the uniform resolvent convergence of the perturbed operator to the homogenized operator and obtain estimates for the rate of convergence. A complete asymptotic expansion is constructed for the resolvent when it acts on sufficiently smooth functions. Bibliography: 41 titles.
Keywords: frequent change, homogenization, uniform resolvent convergence, asymptotic behaviour. 
@article{SM_2014_205_10_a5,
     author = {T. F. Sharapov},
     title = {On the resolvent of multidimensional operators with frequently changing boundary conditions in the case of the homogenized {Dirichlet} condition},
     journal = {Sbornik. Mathematics},
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     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2014_205_10_a5/}
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T. F. Sharapov. On the resolvent of multidimensional operators with frequently changing boundary conditions in the case of the homogenized Dirichlet condition. Sbornik. Mathematics, Tome 205 (2014) no. 10, pp. 1492-1527. http://geodesic.mathdoc.fr/item/SM_2014_205_10_a5/