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Selfadjoint Extensions of the Neumann Laplacian in Domains with Cylindrical Outlets

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Abstract:

Let be a domain with N cylindrical outlets to infinity. The solutions of the Neumann Problem for the Poisson equation are characterized within the theory of self-adjoint extensions of the operator L. Here L is the symmetric operator associated to the problem in , on , in weighted L 2-spaces. The results are applied to examples in the theory of continuum mechanics.

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Authors and Affiliations

  1. State Maritime Academy, Kosaya Liniya, 15-A, St.-Petersburg, 199026, Russia, , , , , , RU

    S.A. Nazarov

  2. Universität Paderborn, 33095 Paderborn, Germany. E-mail: mariasp@uni-paderborn.de, , , , , , DE

    M. Specovius-Neugebauer

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  1. S.A. Nazarov
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  2. M. Specovius-Neugebauer
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Received: 10 June 1996\,/\,Accepted: 16 October 1996

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Nazarov, S., Specovius-Neugebauer, M. Selfadjoint Extensions of the Neumann Laplacian in Domains with Cylindrical Outlets . Comm Math Phys 185, 689–707 (1997). https://doi.org/10.1007/s002200050106

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  • DOI: https://doi.org/10.1007/s002200050106

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