Two-scale convergence of elliptic spectral problems with indefinite density function in perforated domains

Abstract

Spectral asymptotics of linear periodic elliptic operators with indefinite (sign-changing) density function is investigated in perforated domains with the two-scale convergence method. The limiting behavior of positive and negative eigencouples depends crucially on whether the average of the weight over the solid part is positive, negative or equal to zero. We prove concise homogenization results in all three cases.

arXiv comment21 pages. arXiv admin note: substantial text overlap with arXiv:1106.3904

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