Characterizations of diffusion matrices in homogenization of elliptic equations in nondivergence-form
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| Format: | Preprint |
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2022
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| _version_ | 1866929593834799104 |
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| author | Guo, Xiaoqin Sprekeler, Timo Tran, Hung V. |
| author_facet | Guo, Xiaoqin Sprekeler, Timo Tran, Hung V. |
| contents | We characterize diffusion matrices that yield a $L^{\infty}$ convergence rate of $\mathcal{O}(\varepsilon^2)$ in the theory of periodic homogenization of linear elliptic equations in nondivergence-form. Such type-$\varepsilon^2$ diffusion matrices are of particular interest as the optimal rate of convergence in the generic case is only $\mathcal{O}(\varepsilon)$. First, we provide a new class of type-$\varepsilon^2$ diffusion matrices, confirming a conjecture posed in [15]. Then, we give a complete characterization of diagonal diffusion matrices in two dimensions and a systematic study in higher dimensions. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2201_01974 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Characterizations of diffusion matrices in homogenization of elliptic equations in nondivergence-form Guo, Xiaoqin Sprekeler, Timo Tran, Hung V. Analysis of PDEs 35B27, 35B40, 35J25 We characterize diffusion matrices that yield a $L^{\infty}$ convergence rate of $\mathcal{O}(\varepsilon^2)$ in the theory of periodic homogenization of linear elliptic equations in nondivergence-form. Such type-$\varepsilon^2$ diffusion matrices are of particular interest as the optimal rate of convergence in the generic case is only $\mathcal{O}(\varepsilon)$. First, we provide a new class of type-$\varepsilon^2$ diffusion matrices, confirming a conjecture posed in [15]. Then, we give a complete characterization of diagonal diffusion matrices in two dimensions and a systematic study in higher dimensions. |
| title | Characterizations of diffusion matrices in homogenization of elliptic equations in nondivergence-form |
| topic | Analysis of PDEs 35B27, 35B40, 35J25 |
| url | https://arxiv.org/abs/2201.01974 |