Nonlocal vector calculus on the sphere
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915291838021632 |
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| author | Montanelli, Hadrien Slevinsky, Richard Mikael Du, Qiang |
| author_facet | Montanelli, Hadrien Slevinsky, Richard Mikael Du, Qiang |
| contents | We introduce a nonlocal vector calculus on the unit two-sphere using weakly singular integral operators. Within this framework, the operators are diagonalizable in terms of scalar and vector spherical harmonics, a property that facilitates the proof of a nonlocal Stokes theorem. This constitutes the first instance of such a theorem on a curved surface. Furthermore, our analysis demonstrates the strong convergence of these nonlocal operators to the classical differential operators of vector calculus as the interaction range tends to zero. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_12372 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Nonlocal vector calculus on the sphere Montanelli, Hadrien Slevinsky, Richard Mikael Du, Qiang Analysis of PDEs We introduce a nonlocal vector calculus on the unit two-sphere using weakly singular integral operators. Within this framework, the operators are diagonalizable in terms of scalar and vector spherical harmonics, a property that facilitates the proof of a nonlocal Stokes theorem. This constitutes the first instance of such a theorem on a curved surface. Furthermore, our analysis demonstrates the strong convergence of these nonlocal operators to the classical differential operators of vector calculus as the interaction range tends to zero. |
| title | Nonlocal vector calculus on the sphere |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2505.12372 |