Two-scale cut-and-projection convergence for quasiperiodic monotone operators
Averaging certain class of quasiperiodic monotone operators can be simplified to the periodic homogenization setting by mapping the original quasiperiodic structure onto a periodic structure in a higher dimensional space using cut-and projection method. We characterize cut-and-projection convergence...
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Published in | arXiv.org |
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Main Authors | , , |
Format | Paper Journal Article |
Language | English |
Published |
Ithaca
Cornell University Library, arXiv.org
08.06.2022
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Subjects | |
Online Access | Get full text |
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Summary: | Averaging certain class of quasiperiodic monotone operators can be simplified to the periodic homogenization setting by mapping the original quasiperiodic structure onto a periodic structure in a higher dimensional space using cut-and projection method. We characterize cut-and-projection convergence limit of the nonlinear monotone partial differential operator \(-\mathrm{div} \; \sigma\left({\bf x},\frac{{\bf R}{\bf x}}{\eta}, \nabla u_\eta\right)\) for a bounded sequence \(u_\eta\) in \(W^{1,p}_0(\Omega)\), where \(1<p < \infty\), \(\Omega\) is a bounded open subset in \(R^n\) with Lipschitz boundary. We identify the homogenized problem with a local equation defined on the hyperplane in the higher-dimensional space. A new corrector result is established. |
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ISSN: | 2331-8422 |
DOI: | 10.48550/arxiv.2206.03672 |