Quantitative Analysis of Boundary Layers in Periodic Homogenization

Quantitative Analysis of Boundary Layers in Periodic Homogenization

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...

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Veröffentlicht in:Archive for rational mechanics and analysis 2017-11, Vol.226 (2), p.695-741
Hauptverfasser: Armstrong, Scott, Kuusi, Tuomo, Mourrat, Jean-Christophe, Prange, Christophe
Format: Artikel
Sprache:eng
Schlagworte:
Analysis of PDEs
Classical Mechanics
Complex Systems
Fluid- and Aerodynamics
Mathematical and Computational Physics
Mathematics
Physics
Physics and Astronomy
Theoretical
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Zusammenfassung: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.
ISSN:0003-9527
1432-0673
DOI:10.1007/s00205-017-1142-z