Geodesic
Asymptotics of the Solution of the Steklov Spectral Problem in a Domain with a Blunted Peak
Matematičeskie zametki, Tome 86 (2009) no. 4, pp. 571-587.

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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 $O(\varepsilon)$ is broken off. In particular, we establish that any positive eigenvalue with a fixed number turns out to be infinitesimal as $\varepsilon\to+0$ and the corresponding eigenfunction is localized in the $c\varepsilon$-neighborhood of the vertex of the peak.
Keywords: Steklov spectral problem, Laplace operator, domain with a blunted peak, Sobolev space, elliptic boundary-value problem, Neumann problem, Hardy inequality, Poincaré inequality, Green's formula, Hilbert space. 
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S. A. Nazarov. Asymptotics of the Solution of the Steklov Spectral Problem in a Domain with a Blunted Peak. Matematičeskie zametki, Tome 86 (2009) no. 4, pp. 571-587. http://geodesic.mathdoc.fr/item/MZM_2009_86_4_a9/

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