A strong unique continuation result for the Baouendi operator
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866914318419755008 |
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| author | Banerjee, Agnid Garofalo, Nicola |
| author_facet | Banerjee, Agnid Garofalo, Nicola |
| contents | We establish a strong unique continuation property for the subelliptic Baouendi operator under the presence of zero-order perturbations satisfying an almost Hardy-type growth condition. In particular, the admissible class includes both $L^\infty_{\mathrm{loc}}$ and singular potentials. We prove that any solution vanishing to infinite order at a point of the degeneracy manifold of the operator must be identically zero. The result holds extends to variable-coefficient operators with intrinsic Lipschitz regularity. A notable feature of the proof is that it relies exclusively on $L^2$ Carleman estimates combined with the classical Hardy inequality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_09322 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A strong unique continuation result for the Baouendi operator Banerjee, Agnid Garofalo, Nicola Analysis of PDEs We establish a strong unique continuation property for the subelliptic Baouendi operator under the presence of zero-order perturbations satisfying an almost Hardy-type growth condition. In particular, the admissible class includes both $L^\infty_{\mathrm{loc}}$ and singular potentials. We prove that any solution vanishing to infinite order at a point of the degeneracy manifold of the operator must be identically zero. The result holds extends to variable-coefficient operators with intrinsic Lipschitz regularity. A notable feature of the proof is that it relies exclusively on $L^2$ Carleman estimates combined with the classical Hardy inequality. |
| title | A strong unique continuation result for the Baouendi operator |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2602.09322 |