Quantitative analysis of boundary layers in periodic homogenization
Scott Armstrong, Tuomo Kuusi, Jean-Christophe Mourrat, Christophe, Prange
TL;DR
This paper provides optimal convergence rate estimates for boundary layers in periodic homogenization of elliptic systems, improving understanding of how solutions behave near boundaries across various dimensions.
Contribution
It introduces new, optimal convergence estimates for boundary layers in periodic homogenization, applicable in all dimensions, and establishes a regularity estimate for the homogenized boundary condition.
Findings
Optimal convergence rates in dimensions > 3
New estimates in all dimensions
Regularity estimate for boundary condition
Abstract
We prove quantitative estimates on the rate of convergence for the oscillating Dirichlet problem in periodic homogenization of divergence-form uniformly elliptic systems. The estimates are optimal in dimensions larger than three and new in every dimension. We also prove a regularity estimate on the homogenized boundary condition.
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Taxonomy
TopicsAdvanced Mathematical Modeling in Engineering · Composite Material Mechanics · Nonlinear Partial Differential Equations