arXiv subjects

B. Chase Russell

Publications and source records attributed to B. Chase Russell.

2 recordsLinked to original sources

arXiv2018

Quantitative Homogenization with Relatively Soft Inclusions and Interior Estimates

We establish large-scale interior Lipschitz estimates for solutions to systems of linear elasticity with rapidly oscillating periodic coefficients and Dirichlet boundary conditions in domains with periodically placed inclusions of size $\mathcal{O}(\varepsilon)$ and magnitude $δ$ by establishing $H^1$-convergence rates for such solutions. The interior estimates at the macroscopic scale are derived directly without the use of compactness via a Campanato-type scheme presented by S. Armstrong and C.K. Smart and that was adapted for uniformly elliptic equations in by Armstrong and Z. Shen.

math.AP↗

arXiv2017

Homogenization in Perforated Domains and Interior Lipschitz Estimates

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 $\varepsilon$ by establishing $H^1$-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.

math.AP↗