Characterisation of homogenisation for nonlocal diffusion by local topologies
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arXiv
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| Main Authors: | , , , , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866908786101321728 |
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| author | Buchinger, Andreas Burazin, Krešimir Crnjac, Ivana Erceg, Marko Jolić, Maja Waurick, Marcus |
| author_facet | Buchinger, Andreas Burazin, Krešimir Crnjac, Ivana Erceg, Marko Jolić, Maja Waurick, Marcus |
| contents | We consider fractional variants of divergence form problems with highly oscillatory local coefficients. We characterise the convergence of these coefficients by means of classical $H$-convergence covering the local behaviour of the fractional divergence form problem and weak-$\ast$ convergence on the complement caused by the nonlocality of the differential operators. The results are further described in the light of nonlocal $H$-convergence as introduced in [Waurick, Calc Var PDEs, 57, 2018] and certain Schur topologies. Applications to symmetric coefficients and a homogenisation problem for a fractional heat type equation are provided. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_17579 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Characterisation of homogenisation for nonlocal diffusion by local topologies Buchinger, Andreas Burazin, Krešimir Crnjac, Ivana Erceg, Marko Jolić, Maja Waurick, Marcus Analysis of PDEs Primary: 35B27, 35R11, Secondary: 35B40, 74S40 We consider fractional variants of divergence form problems with highly oscillatory local coefficients. We characterise the convergence of these coefficients by means of classical $H$-convergence covering the local behaviour of the fractional divergence form problem and weak-$\ast$ convergence on the complement caused by the nonlocality of the differential operators. The results are further described in the light of nonlocal $H$-convergence as introduced in [Waurick, Calc Var PDEs, 57, 2018] and certain Schur topologies. Applications to symmetric coefficients and a homogenisation problem for a fractional heat type equation are provided. |
| title | Characterisation of homogenisation for nonlocal diffusion by local topologies |
| topic | Analysis of PDEs Primary: 35B27, 35R11, Secondary: 35B40, 74S40 |
| url | https://arxiv.org/abs/2601.17579 |