论文标题
抛物线运营商的类似空间的定量唯一性
Space-like quantitative uniqueness for parabolic operators
论文作者
论文摘要
我们在给定的时间级别获得了尖锐的最大消失订单，以提供$ c {^1} $势$ v $的抛物线方程的解决方案。我们的主要结果定理1.1是Donnelly-Fefferman和Bakri众所周知的抛物线概括。它还提高了朱的先前结果，该结果建立了类似的消失顺序估计值，而随着时间的流逝，它们平均。我们分析中的主要工具是我们在环境中建立的著名粘绿氏菌 - 弗南德斯 - 韦斯氏件类型的新定量版本。
We obtain sharp maximal vanishing order at a given time level for solutions to parabolic equations with a $C{^1}$ potential $V$. Our main result Theorem 1.1 is a parabolic generalization of a well known result of Donnelly-Fefferman and Bakri. It also sharpens a previous result of Zhu that establishes similar vanishing order estimates which are instead averaged over time. The principal tool in our analysis is a new quantitative version of the well-known Escauriaza-Fernandez-Vessella type Carleman estimate that we establish in our setting.
