Localization of Eigenfunctions Near the Vertices in Dirichlet’s Faceted Cup
Sergei Aleksandrovich Nazarov · Functional Analysis and Its Applications · 2026
Abstract We study the spectrum of the Dirichlet problem for the Laplace operator in a thin-walled domain shaped as an upright faceted cup with a regular polygon as the base. We obtain restrictions on the relative thickness of the bottom that ensure localization of the first few eigenfunctions in a neighborhood of the vertices of the base.