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Norm resolvent convergence of Dirichlet Laplacian in unbounded thin waveguides

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Abstract

The proof of norm resolvent convergence of Dirichlet Laplacian to effective operators, as the diameter of spatial waveguides vanishes, is extended to the unbounded case.

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Author information

Authors and Affiliations

  1. Departamento de Matemática – UFSCar, 13560-970, São Carlos, SP, Brazil

    César R. de Oliveira & Alessandra A. Verri

Authors
  1. César R. de Oliveira
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  2. Alessandra A. Verri
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Corresponding author

Correspondence to César R. de Oliveira.

Additional information

The first author acknowledges partial support from CNPq.

The second author was supported by CAPES.

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de Oliveira, C.R., Verri, A.A. Norm resolvent convergence of Dirichlet Laplacian in unbounded thin waveguides. Bull Braz Math Soc, New Series 46, 139–158 (2015). https://doi.org/10.1007/s00574-015-0087-9

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  • DOI: https://doi.org/10.1007/s00574-015-0087-9

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