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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2510.20024 |
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| _version_ | 1866914173133258752 |
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| author | Vincent, Akshara |
| author_facet | Vincent, Akshara |
| contents | We provide counterexamples to uniqueness of solutions as well as a priori Calderón-Zygmund estimates for solutions below $L^2$ using convex integration argument for equations of the type $$ \text{div} (A (\nabla u)) = 0 \quad \text{in } \mathbb{B}^2, $$ where $A: \mathbb{R}^{2} \to \mathbb{R}^2$ is smooth, uniformly elliptic and has essentially linear growth, but fails to be monotone and asymptotically Uhlenbeck. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_20024 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Non-uniqueness and failure of Calderón-Zygmund estimates below the critical exponent for non-monotone PDE with linear growth Vincent, Akshara Analysis of PDEs We provide counterexamples to uniqueness of solutions as well as a priori Calderón-Zygmund estimates for solutions below $L^2$ using convex integration argument for equations of the type $$ \text{div} (A (\nabla u)) = 0 \quad \text{in } \mathbb{B}^2, $$ where $A: \mathbb{R}^{2} \to \mathbb{R}^2$ is smooth, uniformly elliptic and has essentially linear growth, but fails to be monotone and asymptotically Uhlenbeck. |
| title | Non-uniqueness and failure of Calderón-Zygmund estimates below the critical exponent for non-monotone PDE with linear growth |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2510.20024 |