In this note we prove the strong unique continuation property at the origin for the solutions of the parabolic differential inequality

$$\begin{aligned} |\Delta u - u_t| \le \frac{M}{|x|^2} |u|, \end{aligned}$$

with the critical inverse square potential. Our main result sharpens a previous one of Vessella concerned with the subcritical case.

中文翻译：

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具有Hardy型势能的热算子的强唯一连续性

在本文中，我们证明了抛物线不等式不等式解的原点具有很强的唯一连续性

$$ \ begin {aligned} | \ Delta u-u_t | \ le \ frac {M} {| x | ^ 2} | u |，\ end {aligned} $$

具有临界反平方电势。我们的主要结果使Vessella的前一个与亚临界案例有关。