Asymptotics of the solution of the Steklov spectral problem in a domain with a blunted peak
С. А. Назаров · Mathematical Notes · 2009
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.