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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2601.23195 |
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| _version_ | 1866917235550846976 |
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| author | Beck, Lisa Gmeineder, Franz Schäffner, Mathias |
| author_facet | Beck, Lisa Gmeineder, Franz Schäffner, Mathias |
| contents | We establish $\mathrm{W}^{1,1}$-regularity and higher gradient integrability for relaxed minimizers of convex integral functionals on $\mathrm{BV}$. Unlike classical examples such as the minimal surface integrand, we only require linear growth from below but not necessarily from above. This typically comes with a non-uniformly degenerate elliptic behaviour, for which our results extend the presently available bounds from the superlinear growth case in a sharp way. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_23195 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Non-uniformly elliptic variational problems on BV Beck, Lisa Gmeineder, Franz Schäffner, Mathias Analysis of PDEs We establish $\mathrm{W}^{1,1}$-regularity and higher gradient integrability for relaxed minimizers of convex integral functionals on $\mathrm{BV}$. Unlike classical examples such as the minimal surface integrand, we only require linear growth from below but not necessarily from above. This typically comes with a non-uniformly degenerate elliptic behaviour, for which our results extend the presently available bounds from the superlinear growth case in a sharp way. |
| title | Non-uniformly elliptic variational problems on BV |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2601.23195 |