Geodesic
Waveguides with fast oscillating boundary
Nanosistemy: fizika, himiâ, matematika, Tome 8 (2017) no. 2, pp. 160-165

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We consider an elliptic operator in a planar waveguide with a fast oscillating boundary where we impose Dirichlet, Neumann or Robin boundary conditions assuming that both the period and the amplitude of the oscillations are small. We describe the homogenized operator, establish the norm resolvent convergence of the perturbed resolvent to the homogenized one, and prove the estimates for the rate of convergence. It is shown that under the homogenization, the type of the boundary condition can change.
Keywords: elliptic operator, unbounded domain, norm resolvent convergence. 
@article{NANO_2017_8_2_a1,
     author = {G. Cardone},
     title = {Waveguides with fast oscillating boundary},
     journal = {Nanosistemy: fizika, himi\^a, matematika},
     pages = {160--165},
     publisher = {mathdoc},
     volume = {8},
     number = {2},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/NANO_2017_8_2_a1/}
}
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G. Cardone. Waveguides with fast oscillating boundary. Nanosistemy: fizika, himiâ, matematika, Tome 8 (2017) no. 2, pp. 160-165. http://geodesic.mathdoc.fr/item/NANO_2017_8_2_a1/