Estimates on the Laplace Operator in Heat Flows of Harmonic Maps
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910676585283584 |
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| author | Wu, Qingtong |
| author_facet | Wu, Qingtong |
| contents | In this paper we investigate estimates about the Laplace operator in heat flows of harmonic maps, focusing outside the singularities through spherical coordinates. These estimates can be used in the general Ericksen--Leslie system to obtain higher-order estimates. We consider the problem subject to the $\mathbb{T}^2$ and $\mathbb{T}^3$ boundary conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_20419 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Estimates on the Laplace Operator in Heat Flows of Harmonic Maps Wu, Qingtong Analysis of PDEs Mathematical Physics Differential Geometry Functional Analysis In this paper we investigate estimates about the Laplace operator in heat flows of harmonic maps, focusing outside the singularities through spherical coordinates. These estimates can be used in the general Ericksen--Leslie system to obtain higher-order estimates. We consider the problem subject to the $\mathbb{T}^2$ and $\mathbb{T}^3$ boundary conditions. |
| title | Estimates on the Laplace Operator in Heat Flows of Harmonic Maps |
| topic | Analysis of PDEs Mathematical Physics Differential Geometry Functional Analysis |
| url | https://arxiv.org/abs/2410.20419 |