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

Sergei A. Nazarov, Jari Taskinen

Результат исследований: Научные публикации в периодических изданияхстатьярецензирование

2 Цитирования (Scopus)

Аннотация

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.

Язык оригиналаанглийский
Страницы (с-по)2774-2797
Число страниц24
ЖурналJournal of Differential Equations
Том269
Номер выпуска4
DOI
СостояниеОпубликовано - 5 авг 2020

Предметные области Scopus

  • Анализ
  • Прикладная математика

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