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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2412.16131 |
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| _version_ | 1866916536248172544 |
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| author | Beck, Lisa Eitler, Ferdinand Gmeineder, Franz |
| author_facet | Beck, Lisa Eitler, Ferdinand Gmeineder, Franz |
| contents | We establish that locally bounded relaxed minimizers of degenerate elliptic symmetric gradient functionals on $\mathrm{BD}(Ω)$ have weak gradients in $\mathrm{L}_{\mathrm{loc}}^{1}(Ω;\mathbb{R}^{n\times n})$. This is achieved for the sharp ellipticity range that is presently known to yield $\mathrm{W}_{\mathrm{loc}}^{1,1}$-regularity in the full gradient case on $\mathrm{BV}(Ω;\mathbb{R}^{n})$. As a consequence, we also obtain the first Sobolev regularity results for minimizers of the area-type functional on $\mathrm{BD}(Ω)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_16131 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Gradient integrability for bounded $\mathrm{BD}$-minimizers Beck, Lisa Eitler, Ferdinand Gmeineder, Franz Analysis of PDEs 35B65, 35J60, 35J93, 49J45 We establish that locally bounded relaxed minimizers of degenerate elliptic symmetric gradient functionals on $\mathrm{BD}(Ω)$ have weak gradients in $\mathrm{L}_{\mathrm{loc}}^{1}(Ω;\mathbb{R}^{n\times n})$. This is achieved for the sharp ellipticity range that is presently known to yield $\mathrm{W}_{\mathrm{loc}}^{1,1}$-regularity in the full gradient case on $\mathrm{BV}(Ω;\mathbb{R}^{n})$. As a consequence, we also obtain the first Sobolev regularity results for minimizers of the area-type functional on $\mathrm{BD}(Ω)$. |
| title | Gradient integrability for bounded $\mathrm{BD}$-minimizers |
| topic | Analysis of PDEs 35B65, 35J60, 35J93, 49J45 |
| url | https://arxiv.org/abs/2412.16131 |