Asymptotics of the Solution of the Steklov Spectral Problem in a Domain with a Blunted Peak

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.