Differential and Integral Equations

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

Toshiaki Yachimura

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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

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

First available in Project Euclid: 13 June 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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


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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