Steklov problems in perforated domains with a coefficient of indefinite sign
Valeria Chiadò Piat, С. А. Назаров, Andrey Lvovich Piatnitski · Networks and Heterogeneous Media · 2012
We consider homogenization of Steklov spectral problem for adivergence 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.