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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2505.00852 |
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| _version_ | 1866914131819364352 |
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| author | Conti, Sergio Focardi, Matteo Iurlano, Flaviana |
| author_facet | Conti, Sergio Focardi, Matteo Iurlano, Flaviana |
| contents | In this paper we develop the Direct Method in the Calculus of Variations for free-discontinuity energies whose bulk and surface densities exhibit superlinear growth, respectively for large gradients and small jump amplitudes. A distinctive feature of this kind of models is that the functionals are defined on $SBV$ functions whose jump sets may have infinite measure. Establishing general lower semicontinuity and relaxation results in this setting requires new analytical techniques. In addition, we propose a variational approximation of certain superlinear energies via phase field models. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_00852 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Superlinear free-discontinuity models: relaxation and phase field approximation Conti, Sergio Focardi, Matteo Iurlano, Flaviana Analysis of PDEs In this paper we develop the Direct Method in the Calculus of Variations for free-discontinuity energies whose bulk and surface densities exhibit superlinear growth, respectively for large gradients and small jump amplitudes. A distinctive feature of this kind of models is that the functionals are defined on $SBV$ functions whose jump sets may have infinite measure. Establishing general lower semicontinuity and relaxation results in this setting requires new analytical techniques. In addition, we propose a variational approximation of certain superlinear energies via phase field models. |
| title | Superlinear free-discontinuity models: relaxation and phase field approximation |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2505.00852 |