Title: Carleman Estimates for Second Order Elliptic Operators with Limiting Weights, an Elementary Approach Show Chinese title

Title: Carleman 估计用于带有极限权重的二阶椭圆算子，一种简单的方法

Abstract: By using some deep tools from microlocal analysis, the authors of the papers (Ann. of Math., 165 (2007), 567--591, J. Amer. Math. Soc., 23 (2010), 655--691; Invent. Math., 178 (2009), 119--171; Duke Math. J., 158(2011), 83--120) have successfully established various Carleman estimates for elliptic operators that possess limiting Carleman weight. In this study, we revisit these problems and present a unified and fundamental approach for deriving these estimates. The main tool we employ is an elementary pointwise estimate for second-order elliptic operators. Show Chinese abstract

Abstract: 通过使用微局部分析中的一些深度工具，论文作者（Ann. of Math., 165 (2007), 567--591, J. Amer. Math. Soc., 23 (2010), 655--691; Invent. Math., 178 (2009), 119--171; Duke Math. J., 158(2011), 83--120）成功地为具有极限Carleman权重的椭圆算子建立了各种Carleman估计。在本研究中，我们重新审视这些问题，并提出了一种统一且基本的方法来推导这些估计。我们采用的主要工具是二阶椭圆算子的一个基本点态估计。