Ill-posedness of the Dirichlet problem for 2D Lagrangian mean curvature equation
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866917135542910976 |
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| author | Cao, Wentao Wang, Zhehui |
| author_facet | Cao, Wentao Wang, Zhehui |
| contents | We investigate the Dirichlet problem of the two dimensional Lagrangian mean curvature equation in a bounded domain. Infinitely many $C^{1, α} (α\in (0,\frac{1}{5}))$ very weak solutions are built through Nash-Kuiper construction. Moreover, we note there are infinitely many $C^{1, α}$ very weak solutions that can not be improved to be $C^{2, α}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_04816 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Ill-posedness of the Dirichlet problem for 2D Lagrangian mean curvature equation Cao, Wentao Wang, Zhehui Analysis of PDEs We investigate the Dirichlet problem of the two dimensional Lagrangian mean curvature equation in a bounded domain. Infinitely many $C^{1, α} (α\in (0,\frac{1}{5}))$ very weak solutions are built through Nash-Kuiper construction. Moreover, we note there are infinitely many $C^{1, α}$ very weak solutions that can not be improved to be $C^{2, α}$. |
| title | Ill-posedness of the Dirichlet problem for 2D Lagrangian mean curvature equation |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2409.04816 |