$Γ$-convergence of convolution-type functionals for free discontinuity problems
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arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866914420673740800 |
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| author | Brusca, Giuseppe Cosma Donati, Davide Scalabrino, Sergio Trifone, Chiara Voglino, Edoardo |
| author_facet | Brusca, Giuseppe Cosma Donati, Davide Scalabrino, Sergio Trifone, Chiara Voglino, Edoardo |
| contents | We prove compactness with respect to $Γ$-convergence for a general class of non-local energies modelled after the ones considered in [Gobbino, CPAM (1998)]. We give an integral representation result for the limits, which are free discontinuity functionals defined on the space of generalised special functions of bounded variation. We then characterise the bulk and surface energy densities of the obtained limits by means of minimisation problems on small cubes for the approximating energies. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_24192 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | $Γ$-convergence of convolution-type functionals for free discontinuity problems Brusca, Giuseppe Cosma Donati, Davide Scalabrino, Sergio Trifone, Chiara Voglino, Edoardo Analysis of PDEs Optimization and Control 49J45, 49Q20, 65K10 We prove compactness with respect to $Γ$-convergence for a general class of non-local energies modelled after the ones considered in [Gobbino, CPAM (1998)]. We give an integral representation result for the limits, which are free discontinuity functionals defined on the space of generalised special functions of bounded variation. We then characterise the bulk and surface energy densities of the obtained limits by means of minimisation problems on small cubes for the approximating energies. |
| title | $Γ$-convergence of convolution-type functionals for free discontinuity problems |
| topic | Analysis of PDEs Optimization and Control 49J45, 49Q20, 65K10 |
| url | https://arxiv.org/abs/2603.24192 |