najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМО10.17586/2220-8054-2017-8-2-160-165najo-644Research ArticleMATHEMATICSМАТЕМАТИКАWaveguides with fast oscillating boundaryCardoneG.

Department of Engineering

Corso Garibaldi, 107, 82100 Benevento

gcardone@unisannio.itUniversity of SannioItaly20171208202582160165Copyright © Cardone G., 20252025Cardone G.Cardone G.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://nanojournal.ifmo.ru/jour/article/view/644

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.

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The authors declare that there are no conflicts of interest present.