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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/2403.20265 |
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| _version_ | 1866910390872440832 |
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| author | Kleiner, Bruce Müller, Stefan Székelyhidi Jr., László Xie, Xiangdong |
| author_facet | Kleiner, Bruce Müller, Stefan Székelyhidi Jr., László Xie, Xiangdong |
| contents | We develop a general toolbox to study $W^{1,p}$ solutions of differential inclusions $\nabla u \in K$ for unbounded sets $K$. A key notion is the concept that a subset $K$ of the space $\mathbb{R}^{d \times m}$ of $d \times m$ matrices can be reduced to another set $K'$. We then use this framework to show that the product rigidity for Sobolev maps fails for $p<2$, and also apply our toolbox to simplify several examples from the literature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_20265 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Rigidity of Euclidean product structure: breakdown for low Sobolev exponents Kleiner, Bruce Müller, Stefan Székelyhidi Jr., László Xie, Xiangdong Analysis of PDEs We develop a general toolbox to study $W^{1,p}$ solutions of differential inclusions $\nabla u \in K$ for unbounded sets $K$. A key notion is the concept that a subset $K$ of the space $\mathbb{R}^{d \times m}$ of $d \times m$ matrices can be reduced to another set $K'$. We then use this framework to show that the product rigidity for Sobolev maps fails for $p<2$, and also apply our toolbox to simplify several examples from the literature. |
| title | Rigidity of Euclidean product structure: breakdown for low Sobolev exponents |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2403.20265 |