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Bulk-surface spectral homogenization with indefinite mass in periodic perforated domains
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 dSy is indefinite. We show that the asymptotic behavior of the spectrum depends essentially on whether the combined mean meff=∫Y*q dy+∫Γρ dSy 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(ε) estimates for the shifted or rescaled eigenvalues, spectral projectors, and aligned eigenspaces.
Related
- Surface-to-Volume Homogenization of NonLinear Steklov Eigencouples with NonHomogeneous Orlicz Growth in Perforated Domains
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- Homogenization of an optimal control problem for a Navier-Stokes-Cahn-Hilliard system in a 3D perforated domain
BibTeX
@misc{douanla2026bulksurface,
title = {{Bulk-surface spectral homogenization with indefinite mass in periodic perforated domains}},
author = {Hermann DOUANLA},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.05487},
eprint = {2610.05487},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.05487},
}
RIS
TY - UNPB
TI - Bulk-surface spectral homogenization with indefinite mass in periodic perforated domains
AU - Hermann DOUANLA
PY - 2026
DA - 2026/10/04
PB - arXiv
DO - 10.48550/arxiv.2610.05487
UR - https://arxiv.org/abs/2610.05487
AB - 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_eff=∫_Y^*q dy+∫_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(ε) estimates for the shifted or rescaled eigenvalues, spectral projectors, and aligned eigenspaces.
ER -