Gamma-convergence as $s\to1^-$ of anisotropic nonlocal fractional perimeter functionals
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912590525890560 |
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| author | Fanizza, Alberto |
| author_facet | Fanizza, Alberto |
| contents | We investigate the asymptotic behavior in the sense of $Γ(L^1_{loc})$-convergence as $s\to1^-$ of anisotropic non local $s$-fractional perimeters defined with respect to general anisotropic integration kernels $k_s(\cdot)$, under the hypothesis of pointwise convergence of such kernels. In particular, we prove the $Γ(L^1_{loc})$-convergence as $s\to1^-$ of the rescaled anisotropic nonlocal $s$-fractional perimeters defined with respect to the kernels $k_s(\cdot)$ to a suitable anisotropic perimeter. We do so both in $\mathbb{R}^n$ and on a bounded domain $Ω\subset\mathbb{R}^n$ with Lipschitz boundary. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_13823 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Gamma-convergence as $s\to1^-$ of anisotropic nonlocal fractional perimeter functionals Fanizza, Alberto Analysis of PDEs 49Q20 (Primary) 52A38, 28A75 (Secondary) We investigate the asymptotic behavior in the sense of $Γ(L^1_{loc})$-convergence as $s\to1^-$ of anisotropic non local $s$-fractional perimeters defined with respect to general anisotropic integration kernels $k_s(\cdot)$, under the hypothesis of pointwise convergence of such kernels. In particular, we prove the $Γ(L^1_{loc})$-convergence as $s\to1^-$ of the rescaled anisotropic nonlocal $s$-fractional perimeters defined with respect to the kernels $k_s(\cdot)$ to a suitable anisotropic perimeter. We do so both in $\mathbb{R}^n$ and on a bounded domain $Ω\subset\mathbb{R}^n$ with Lipschitz boundary. |
| title | Gamma-convergence as $s\to1^-$ of anisotropic nonlocal fractional perimeter functionals |
| topic | Analysis of PDEs 49Q20 (Primary) 52A38, 28A75 (Secondary) |
| url | https://arxiv.org/abs/2509.13823 |