Regularity for Hamiltonian stationary equations in $\mathbb{R}_{n\leq 4}^{n}$
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913811973275648 |
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| author | Bhattacharya, Arunima |
| author_facet | Bhattacharya, Arunima |
| contents | In this paper, we study the regularity of solutions to the Hamiltonian stationary equation in complex Euclidean space. We show that in dimensions $n\leq 4$, for all values of the Lagrangian phase, any $C^{1,1}$ solution is smooth and derive a $C^{k,α}$ estimate for it, where $k \geq 2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_18013 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Regularity for Hamiltonian stationary equations in $\mathbb{R}_{n\leq 4}^{n}$ Bhattacharya, Arunima Analysis of PDEs Differential Geometry In this paper, we study the regularity of solutions to the Hamiltonian stationary equation in complex Euclidean space. We show that in dimensions $n\leq 4$, for all values of the Lagrangian phase, any $C^{1,1}$ solution is smooth and derive a $C^{k,α}$ estimate for it, where $k \geq 2$. |
| title | Regularity for Hamiltonian stationary equations in $\mathbb{R}_{n\leq 4}^{n}$ |
| topic | Analysis of PDEs Differential Geometry |
| url | https://arxiv.org/abs/2504.18013 |