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Elliptic problems in thin domains with highly oscillating boundaries

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Abstract

We study the Laplace operator with Neumann boundary conditions in a 2-dimensional thin domain with a higly oscillating boundary. We obtain the correct limit problem for the case where the boundary is the graph of the oscillating function ϵG ϵ(x) where G ϵ(x) = a(x) + b(x)g(x/ϵ) with g periodic and a and b not necessarily constant.

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References

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Authors and Affiliations

  1. Dpto. Matematica Aplicada, Universidad Complutense de Madrid, 28040, Madrid, Spain

    José M. Arrieta

  2. Escola de Artes, Ciencias e Humanidades, Universidade de São Paulo, São Paulo, Brasil

    Marcone C. Pereira

Authors
  1. José M. Arrieta
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  2. Marcone C. Pereira
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Corresponding author

Correspondence to José M. Arrieta.

Additional information

Partially supported by: PHB2006-003 PC and PR2009-0027 from MICINN; MTM2006-08262, MTM2009-07540 DGES, Spain and GR58/08, Grupo 920894 (BSCH-UCM, Spain)

Partially supported by FAPESP 2006/06278-7, CAPES DGU 127/07 and CNPq 305210/2008-4.

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Arrieta, J.M., Pereira, M.C. Elliptic problems in thin domains with highly oscillating boundaries. SeMA 51, 17–24 (2010). https://doi.org/10.1007/BF03322549

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