First-order expansion for the Dirichlet eigenvalues of an elliptic system with oscillating coefficients

This paper is concerned with the homogenization of the Dirichlet eigenvalue problem, posed in a bounded domain Ω ⊂ R, for a vectorial elliptic operator −∇·A(·)∇ with ε-periodic coefficients. We analyse the asymptotics of the eigenvalues λ when ε → 0, the mode k being fixed. A first-order asymptotic expansion is proved for λ in the case when Ω is either a… CONTINUE READING