Localization of Eigenfunctions of the Laplace Operator in a Domain with a Perforated Barrier


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The localization of eigenfunctions of the Laplace operator in a domain divided by a perforated barrier is proven. The localization takes place with sufficiently small holes in the barrier. In this case, the measure of the barrier can be arbitrarily small.

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A. Delitsyn

Institute for Information Transmission Problems, Russian Academy of Sciences; Main Scientific Research Test Center of Robotics, Ministry of Defense of the Russian Federation

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Email: delitsyn@mail.ru
Rússia, Moscow, 127051; Moscow, 119001

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