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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2412.16131 |
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Table of 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 $\mathrm{BD}(Ω)$.