Homogenization of Steklov spectral problems with indefinite density function in perforated domains
Artikel i vetenskaplig tidskrift, 2013

The asymptotic behavior of second order self-adjoint elliptic Steklov eigenvalue problems with periodic rapidly oscillating coefficients and with indefinite (sign-changing) density function is investigated in periodically perforated domains. We prove that the spectrum of this problem is discrete and consists of two sequences, one tending to −∞ and another to +∞. The limiting behavior of positive and negative eigencouples depends crucially on whether the average of the weight over the surface of the reference hole is positive, negative or equal to zero. By means of the two-scale convergence method, we investigate all three cases.

Perforated domains

Eigenvalue problems


Two-scale convergence

Indefinite weight function


Hermann Douanla Yonta

Chalmers, Matematiska vetenskaper, Matematik

Göteborgs universitet

Acta Applicandae Mathematicae

0167-8019 (ISSN) 1572-9036 (eISSN)

Vol. 123 261-284


Matematisk analys