论文标题
$ \ bar \ partial $带有方形积分潜力的唯一延续
Unique continuation for $\bar\partial$ with square-integrable potentials
论文作者
论文摘要
在本文中，我们调查了不平等的唯一延续属性$ | \ bar \ partial u | \ le v | u | $，其中$ u $是$ \ mathbb c^n $ in $ \ mathbb c^n $的vector值函数，以及l^2 $中的潜在$ v \。我们表明，当$ n = 1 $时，强大的唯一延续属性具有较弱的独特延续属性时，当$ n \ ge 2 $时就会成立。在这两种情况下，电势上的$ l^2 $令人愉快的条件都是最佳的。
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.
