Abstract
We construct and justify the asymptotics of the eigenvalues and eigenfunctions of the Laplace equation with Steklov boundary conditions in a domain with an acute peak whose end of size O(ɛ) is broken off. In particular, we establish that any positive eigenvalue with a fixed number turns out to be infinitesimal as ɛ → +0 and the corresponding eigenfunction is localized in the cɛ-neighborhood of the vertex of the peak.
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