Hardy decomposition of first order Lipschitz functions by Lamé-Navier solutions
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866912809730703360 |
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| author | Santiesteban, Daniel Alfonso Blaya, Ricardo Abreu Alpay, Daniel |
| author_facet | Santiesteban, Daniel Alfonso Blaya, Ricardo Abreu Alpay, Daniel |
| contents | The Clifford algebra language allows us to rewrite the Lamé-Navier system in terms of the Euclidean Dirac operator. In this paper, the main question we shall be concerned with is whether or not a higher order Lipschitz function on the boundary $Γ$ of a Jordan domain $Ω\subset\mathbb{R}^m$ can be decomposed into a sum of the two boundary values of a solution of the Lamé-Navier system with jump across $Γ$. Our main tool are the Hardy projections related to a singular integral operator arising in the context of Clifford analysis, which turns out to be an involution operator on the first order Lipschitz classes. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_04528 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Hardy decomposition of first order Lipschitz functions by Lamé-Navier solutions Santiesteban, Daniel Alfonso Blaya, Ricardo Abreu Alpay, Daniel Analysis of PDEs Mathematical Physics 30G35 The Clifford algebra language allows us to rewrite the Lamé-Navier system in terms of the Euclidean Dirac operator. In this paper, the main question we shall be concerned with is whether or not a higher order Lipschitz function on the boundary $Γ$ of a Jordan domain $Ω\subset\mathbb{R}^m$ can be decomposed into a sum of the two boundary values of a solution of the Lamé-Navier system with jump across $Γ$. Our main tool are the Hardy projections related to a singular integral operator arising in the context of Clifford analysis, which turns out to be an involution operator on the first order Lipschitz classes. |
| title | Hardy decomposition of first order Lipschitz functions by Lamé-Navier solutions |
| topic | Analysis of PDEs Mathematical Physics 30G35 |
| url | https://arxiv.org/abs/2601.04528 |