Periodic homogenization of convolution type operators with irregular Lévy type tails
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866911614876254208 |
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| author | Jin, Xiaofeng Huo, Wentao Ma, Lingwei Zhang, Zhenqiu |
| author_facet | Jin, Xiaofeng Huo, Wentao Ma, Lingwei Zhang, Zhenqiu |
| contents | We establish the homogenization results for a class of nonlocal operators of convolution type with integrable jumping kernel $p$ multiplied by rapidly oscillating periodic or locally periodic coefficients. The associated measure $p(z)dz$ is assumed to belong to the domain of attraction of a symmetric $α$-stable law. We also assume that $p$ satisfies a pointwise Lévy type lower bound and an averaged annular upper bound for points bounded away from the origin, and that the local $L^1$ oscillation of $p$ decays faster at infinity than its local $L^1$-norm. Under these assumptions, we prove the resolvent convergence of the nonlocal operators and explicitly determine the corresponding homogenized nonlocal operator, which is shown to be comparable to the fractional Laplacian. The proof relies on compactness arguments and a refined analysis based on the annular integral upper bound and an $\varepsilon$-cube decomposition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_20550 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Periodic homogenization of convolution type operators with irregular Lévy type tails Jin, Xiaofeng Huo, Wentao Ma, Lingwei Zhang, Zhenqiu Analysis of PDEs 35B27, 47G10, 45P05, 45M05 We establish the homogenization results for a class of nonlocal operators of convolution type with integrable jumping kernel $p$ multiplied by rapidly oscillating periodic or locally periodic coefficients. The associated measure $p(z)dz$ is assumed to belong to the domain of attraction of a symmetric $α$-stable law. We also assume that $p$ satisfies a pointwise Lévy type lower bound and an averaged annular upper bound for points bounded away from the origin, and that the local $L^1$ oscillation of $p$ decays faster at infinity than its local $L^1$-norm. Under these assumptions, we prove the resolvent convergence of the nonlocal operators and explicitly determine the corresponding homogenized nonlocal operator, which is shown to be comparable to the fractional Laplacian. The proof relies on compactness arguments and a refined analysis based on the annular integral upper bound and an $\varepsilon$-cube decomposition. |
| title | Periodic homogenization of convolution type operators with irregular Lévy type tails |
| topic | Analysis of PDEs 35B27, 47G10, 45P05, 45M05 |
| url | https://arxiv.org/abs/2604.20550 |