We consider homogenization of Steklov spectral problem for a divergence form elliptic operator in periodically perforated domain under the assumption that the spectral weight function changes sign. We show that the limit behaviour of the spectrum depends essentially on wether the average of the weight function over the boundary of holes is positive, or negative or equal to zero. In all these cases we construct the asymptotics of the eigenpairs.

Steklov problems in perforated domains with a coefficient of indefinite sign / CHIADO' PIAT, Valeria; S., Nazarov; A., Piatnitski. - In: NETWORKS AND HETEROGENEOUS MEDIA. - ISSN 1556-1801. - STAMPA. - 7:1(2012), pp. 151-178. [10.3934/nhm.2012.7.151]

Steklov problems in perforated domains with a coefficient of indefinite sign

CHIADO' PIAT, Valeria;
2012

Abstract

We consider homogenization of Steklov spectral problem for a divergence form elliptic operator in periodically perforated domain under the assumption that the spectral weight function changes sign. We show that the limit behaviour of the spectrum depends essentially on wether the average of the weight function over the boundary of holes is positive, or negative or equal to zero. In all these cases we construct the asymptotics of the eigenpairs.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11583/2504510
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