Periodic and stochastic homogenization of general nonlocal operators with oscillating coefficients
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| Main Authors: | , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866911592990375936 |
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| author | Jin, Xiaofeng Huo, Wentao Ma, Lingwei Zhang, Zhenqiu |
| author_facet | Jin, Xiaofeng Huo, Wentao Ma, Lingwei Zhang, Zhenqiu |
| contents | This paper investigates homogenization problems for the nonlocal operators with rapidly oscillating coefficients in the cases of periodic and random statistically homogeneous micro-structures. These operators involve the fractional Laplacian and some operators compared to it. Based on the $Γ$-convergence method and compactness arguments, we prove the homogenization theorems for these nonlocal operators with product-type and symmetric coefficient-structured kernels respectively. Furthermore, these results are extended to general nonlinear nonlocal equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_12845 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Periodic and stochastic homogenization of general nonlocal operators with oscillating coefficients Jin, Xiaofeng Huo, Wentao Ma, Lingwei Zhang, Zhenqiu Analysis of PDEs 35B27, 47G20, 60H25, 45M05 This paper investigates homogenization problems for the nonlocal operators with rapidly oscillating coefficients in the cases of periodic and random statistically homogeneous micro-structures. These operators involve the fractional Laplacian and some operators compared to it. Based on the $Γ$-convergence method and compactness arguments, we prove the homogenization theorems for these nonlocal operators with product-type and symmetric coefficient-structured kernels respectively. Furthermore, these results are extended to general nonlinear nonlocal equations. |
| title | Periodic and stochastic homogenization of general nonlocal operators with oscillating coefficients |
| topic | Analysis of PDEs 35B27, 47G20, 60H25, 45M05 |
| url | https://arxiv.org/abs/2604.12845 |