Surface-to-Volume Homogenization of NonLinear Steklov Eigencouples with NonHomogeneous Orlicz Growth in Perforated Domains
Abstract
We study normalized principal Steklov eigencouples on periodically perforated domains when both the bulk energy and the boundary normalization have general, possibly nonhomogeneous, Orlicz growth. The surface term on the hole boundaries carries the critical surface-to-volume scaling. For each fixed mass level, the constrained minima converge along the whole family, while selected minimizers, fluxes and Lagrange multipliers converge along subsequences to the corresponding objects of a homogenized problem. In the limit, the bulk operator is given by a convex cell problem, and the boundary term becomes a volume term weighted by the total surface density of the reference hole. The key tool is a strong approximation of the microscopic traces by cell averages, measured in the scaled surface modular.
Related
- Homogenization of degenerate parabolic equations with nonlinear Robin reactions in perforated domains
- Bulk-surface spectral homogenization with indefinite mass in periodic perforated domains
- Homogenization of the Stokes equations in a domain perforated by a thin truss
- Critical homogenization of the Navier--Stokes--Cahn--Hilliard system in perforated domains
- Homogenization of an optimal control problem for a Navier-Stokes-Cahn-Hilliard system in a 3D perforated domain
BibTeX
@misc{douanla2026surfacetovolume,
title = {{Surface-to-Volume Homogenization of NonLinear Steklov Eigencouples with NonHomogeneous Orlicz Growth in Perforated Domains}},
author = {Hermann Douanla and Hubert Nnang and Joel Fotso Tachago and Jean Louis Woukeng},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.16693},
eprint = {2610.16693},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.16693},
}
RIS
TY - UNPB
TI - Surface-to-Volume Homogenization of NonLinear Steklov Eigencouples with NonHomogeneous Orlicz Growth in Perforated Domains
AU - Hermann Douanla
AU - Hubert Nnang
AU - Joel Fotso Tachago
AU - Jean Louis Woukeng
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2610.16693
UR - https://arxiv.org/abs/2610.16693
AB - We study normalized principal Steklov eigencouples on periodically perforated domains when both the bulk energy and the boundary normalization have general, possibly nonhomogeneous, Orlicz growth. The surface term on the hole boundaries carries the critical surface-to-volume scaling. For each fixed mass level, the constrained minima converge along the whole family, while selected minimizers, fluxes and Lagrange multipliers converge along subsequences to the corresponding objects of a homogenized problem. In the limit, the bulk operator is given by a convex cell problem, and the boundary term becomes a volume term weighted by the total surface density of the reference hole. The key tool is a strong approximation of the microscopic traces by cell averages, measured in the scaled surface modular.
ER -