Non-local approximation of free-discontinuity problems in linear elasticity and application to stochastic homogenisation
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866912124994846720 |
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| author | Marziani, Roberta Solombrino, Francesco |
| author_facet | Marziani, Roberta Solombrino, Francesco |
| contents | We analyse the $Γ$-convergence of general non-local convolution type functionals with varying densities depending on the space variable and on the symmetrized gradient. The limit is a local free-discontinuity functional, where the bulk term can be completely characterized in terms of an asymptotic cell formula. From that, we can deduce an homogenisation result in the stochastic setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_13759 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Non-local approximation of free-discontinuity problems in linear elasticity and application to stochastic homogenisation Marziani, Roberta Solombrino, Francesco Analysis of PDEs Functional Analysis 49J45, 49Q20, 74Q05, 74R10, 70G75 We analyse the $Γ$-convergence of general non-local convolution type functionals with varying densities depending on the space variable and on the symmetrized gradient. The limit is a local free-discontinuity functional, where the bulk term can be completely characterized in terms of an asymptotic cell formula. From that, we can deduce an homogenisation result in the stochastic setting. |
| title | Non-local approximation of free-discontinuity problems in linear elasticity and application to stochastic homogenisation |
| topic | Analysis of PDEs Functional Analysis 49J45, 49Q20, 74Q05, 74R10, 70G75 |
| url | https://arxiv.org/abs/2212.13759 |