Differential and Integral Equations

Two-phase eigenvalue problem on thin domains with Neumann boundary condition

Toshiaki Yachimura

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Abstract

In this paper, we study an eigenvalue problem with piecewise constant coefficients on thin domains with Neumann boundary condition, and we analyze the asymptotic behavior of each eigenvalue as the domain degenerates into a certain hypersurface being the set of discontinuities of the coefficients. We show how the discontinuity of the coefficients and the geometric shape of the interface affect the asymptotic behavior of the eigenvalues by using a variational approach.

Article information

Source
Differential Integral Equations, Volume 31, Number 9/10 (2018), 735-760.

Dates
First available in Project Euclid: 13 June 2018

Permanent link to this document
https://projecteuclid.org/euclid.die/1528855438

Mathematical Reviews number (MathSciNet)
MR3814565

Zentralblatt MATH identifier
06945780

Subjects
Primary: 35J20: Variational methods for second-order elliptic equations 35P20: Asymptotic distribution of eigenvalues and eigenfunctions

Citation

Yachimura, Toshiaki. Two-phase eigenvalue problem on thin domains with Neumann boundary condition. Differential Integral Equations 31 (2018), no. 9/10, 735--760. https://projecteuclid.org/euclid.die/1528855438


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