Research output: Contribution to journal › Article › peer-review
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 language | English |
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Pages (from-to) | 2774-2797 |
Number of pages | 24 |
Journal | Journal of Differential Equations |
Volume | 269 |
Issue number | 4 |
DOIs | |
State | Published - 5 Aug 2020 |
ID: 60873544