Abstract
We deal with the eigenvalues of the Laplacian in a domain with a thin tubular hole. We impose the Robin or the Neumann B.C on the boundary of the hole and investigate the detailed asymptotic behavior of the eigenvalues when the hole becomes thinner and shrinks to a lower dimensional manifold.
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Research supported by Grant-in-Aid Science Research (C) No 22540216, JSPS.
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Jimbo, S. Eigenvalues of the Laplacian in a Domain With a Thin Tubular Hole. J Elliptic Parabol Equ 1, 137–174 (2015). https://doi.org/10.1007/BF03377373
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DOI: https://doi.org/10.1007/BF03377373