A strong unique continuation result for the Baouendi operator

TL;DR

This paper proves a strong unique continuation property for the Baouendi operator, including cases with zero-order perturbations and variable coefficients, using $L^2$ Carleman estimates and Hardy inequalities.

Contribution

It establishes the first strong unique continuation result for the Baouendi operator with broad classes of potentials and variable coefficients, expanding previous understanding.

Findings

Unique continuation holds for solutions vanishing to infinite order.

Applicable to $L^ abla_{ ext{loc}}$ and singular potentials.

Extends to variable-coefficient operators with Lipschitz regularity.

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.