Localization of eigenfunctions in a thin cylinder with a locally periodic oscillating boundary
Journal article, 2022

We study a Dirichlet spectral problem for a second-order elliptic operator with locally periodic coefficients in a thin cylinder. The lateral boundary of the cylinder is assumed to be locally periodic. When the thickness of the cylinder ε tends to zero, the eigenvalues are of order ε−2 and described in terms of the first eigenvalue μ(x1) of an auxiliary spectral cell problem parametrized by x1, while the eigenfunctions localize with rate ε.

Dimension reduction

Localization of eigenfunctions

Thin domains

Locally periodic structure



Klas Pettersson

Chalmers, Microtechnology and Nanoscience (MC2), Quantum Technology

Journal of Mathematical Analysis and Applications

0022-247X (ISSN) 1096-0813 (eISSN)

Vol. 511 1 126074

Subject Categories

Computational Mathematics

Other Physics Topics

Mathematical Analysis



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