2017/04/11 by B. Chase Russell, Russell, B. Chase
Computer Science · Engineering · #35B27 #74B05 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Composite Material Mechanics #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.1704.03398
openalex publication_date 2017/04/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We establish interior Lipschitz estimates at the macroscopic scale for solutions to systems of linear elasticity with rapidly oscillating periodic coefficients and mixed boundary conditions in domains periodically perforated at a microscopic scale ε by establishing H1-convergence rates for such solutions. The interior estimates are derived directly without the use of compactness via an argument presented in [3] that was adapted for elliptic equations in [2] and [11]. As a consequence, we derive a Liouville type estimate for solutions to the systems of linear elasticity in unbounded periodically perforated domains.