“Blinking eigenvalues” of the Steklov problem generate the continuous spectrum in a cuspidal domain

Sergei A. Nazarov, Jari Taskinen

Research output

1 Citation (Scopus)

Abstract

We study the Steklov spectral problem for the Laplace operator in a bounded domain Ω⊂Rd, d≥2, with a cusp such that the continuous spectrum of the problem is non-empty, and also in the family of bounded domains Ωε⊂Ω, ε>0, obtained from Ω by blunting the cusp at the distance of ε from the cusp tip. While the spectrum in the blunted domain Ωε consists for a fixed ε of an unbounded positive sequence {λj ε}j=1 of eigenvalues, we single out different types of behavior of some eigenvalues as ε→+0: in particular, stable, blinking, and gliding families of eigenvalues are found. We also describe a mechanism which transforms the family of the eigenvalue sequences into the continuous spectrum of the problem in Ω, when ε→+0.

Original languageEnglish
Pages (from-to)2774-2797
Number of pages24
JournalJournal of Differential Equations
Volume269
Issue number4
DOIs
Publication statusPublished - 5 Aug 2020

Scopus subject areas

  • Analysis
  • Applied Mathematics

Fingerprint Dive into the research topics of '“Blinking eigenvalues” of the Steklov problem generate the continuous spectrum in a cuspidal domain'. Together they form a unique fingerprint.

  • Cite this