Quantitative Homogenization and Uniform Lipschitz Estimates for Lamé-Stokes Systems
Abstract
We study homogenization of Lamé-Stokes systems with fixed material parameters. Incompressible elastic inclusions are periodically distributed in a connected elastic matrix, with an elastic buffer near the outer boundary. The divergence constraint acts only in the inclusions, and the full pressure contributes to interface traction. We identify the effective elasticity system for the traction problem of period ε. Under the respective regularity assumptions, we obtain the optimal O(ε) convergence rate for the displacement in L2. For the unsmoothed first-order approximation, the displacement error in H1 and the pressure error in L2 over the inclusions are both O(ε1/2). For a C1,1 outer boundary, both errors improve to O(ε) on every fixed interior subdomain. We establish local interface Schauder estimates including the full pressure and combine them with large-scale iteration to obtain Lipschitz estimates for the displacement up to the boundary and L∞ bounds for the pressure in the inclusions. These Lipschitz and pressure bounds are uniform in ε for C1,κ interfaces and outer boundary and compatible C0,τ traction data, where 0<τ<κ<1.
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BibTeX
@misc{wang2026quantitative,
title = {{Quantitative Homogenization and Uniform Lipschitz Estimates for Lamé-Stokes Systems}},
author = {Beichen Wang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2606.05098},
eprint = {2606.05098},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.05098},
}
RIS
TY - UNPB
TI - Quantitative Homogenization and Uniform Lipschitz Estimates for Lamé-Stokes Systems
AU - Beichen Wang
PY - 2026
DA - 2026/10/24
PB - arXiv
DO - 10.48550/arxiv.2606.05098
UR - https://arxiv.org/abs/2606.05098
AB - We study homogenization of Lamé-Stokes systems with fixed material parameters. Incompressible elastic inclusions are periodically distributed in a connected elastic matrix, with an elastic buffer near the outer boundary. The divergence constraint acts only in the inclusions, and the full pressure contributes to interface traction. We identify the effective elasticity system for the traction problem of period ε. Under the respective regularity assumptions, we obtain the optimal O(ε) convergence rate for the displacement in L^2. For the unsmoothed first-order approximation, the displacement error in H^1 and the pressure error in L^2 over the inclusions are both O(ε^1/2). For a C^1,1 outer boundary, both errors improve to O(ε) on every fixed interior subdomain. We establish local interface Schauder estimates including the full pressure and combine them with large-scale iteration to obtain Lipschitz estimates for the displacement up to the boundary and L^∞ bounds for the pressure in the inclusions. These Lipschitz and pressure bounds are uniform in ε for C^1,κ interfaces and outer boundary and compatible C^0,τ traction data, where 0<τ<κ<1.
ER -