Quantitative Homogenization with Relatively Soft Inclusions and Interior Estimates

B. Chase Russell

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arXiv · 1805.05183

Quantitative Homogenization with Relatively Soft Inclusions and Interior Estimates

B. Chase Russell

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Abstract

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 $\delta$ 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.

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B. Chase Russell. 2018-05-10. Quantitative Homogenization with Relatively Soft Inclusions and Interior Estimates. https://arxiv.org/abs/1805.05183

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