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arXiv · 2610.05487

Bulk-surface spectral homogenization with indefinite mass in periodic perforated domains

Hermann DOUANLA
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Abstract

We study the homogenization of an elliptic eigenvalue problem in a periodically perforated domain, where the spectral parameter appears both in the equation, through a bulk density $q$, and in a Steklov condition on the boundaries of the holes, through a surface density $ρ$, and where the resulting bulk--surface spectral measure $q\,dy+ρ\,dS_y$ is indefinite. We show that the asymptotic behavior of the spectrum depends essentially on whether the combined mean $m_{\rm eff}=\int_{Y^*}q\,dy+\int_Γρ\,dS_y$ is positive, negative, or zero. In all three cases, we prove convergence of eigenvalue clusters with multiplicity and of eigenspaces and, under additional regularity, $O(\varepsilon)$ estimates for the shifted or rescaled eigenvalues, spectral projectors, and aligned eigenspaces.

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Hermann DOUANLA. 2026-10-04. Bulk-surface spectral homogenization with indefinite mass in periodic perforated domains. https://arxiv.org/abs/2610.05487

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