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arXiv · 2203.04346

Unique continuation for $\bar\partial$ with square-integrable potentials

Yifei Pan·Yuan Zhang
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Abstract

In this paper, we investigate the unique continuation property for the inequality $|\bar\partial u| \le V|u|$, where $u$ is a vector-valued function from a domain in $\mathbb C^n$ to $\mathbb C^N$, and the potential $V\in L^2$. We show that the strong unique continuation property holds when $n=1$, and the weak unique continuation property holds when $n\ge 2$. In both cases, the $L^2$ integrability condition on the potential is optimal.

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Yifei Pan, Yuan Zhang. 2022-03-08. Unique continuation for $\bar\partial$ with square-integrable potentials. https://arxiv.org/abs/2203.04346

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