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arXiv · 2602.09322

A strong unique continuation result for the Baouendi operator

Agnid Banerjee·Nicola Garofalo
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Abstract

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.

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Agnid Banerjee, Nicola Garofalo. 2026-02-10. A strong unique continuation result for the Baouendi operator. https://arxiv.org/abs/2602.09322

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