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


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Abstract

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.

About the authors

A. L. Delitsyn

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

Author for correspondence.
Email: delitsyn@mail.ru
Russian Federation, Moscow, 127051; Moscow, 119001

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