论文标题
卡尔曼估计一类可变系数退化椭圆运算符，并应用于独特的延续
Carleman estimates for a class of variable coefficient degenerate elliptic operators with applications to unique continuation
论文作者
论文摘要
在本文中，我们获得了一类可变系数退化椭圆运算符的新卡尔曼估计，其恒定系数模型在一个点上是所谓的Baouendi-Grushin运算符。这概括了我们两个人在[9]中使用Garofalo获得的结果，在[9]中为“恒定系数” Baouendi-Grushin操作员建立了类似的估计。因此，我们获得了：（i）可变系数设置中的波尔加因 - kenig型定量唯一性； （ii）以及一类退化sublinear方程的强大独特延续性。我们还在欧几里得环境中通过Regbaoui在欧几里得的设置中证明了缩放量表的关键卡尔曼估计值的次细胞版本，我们在扩展关键强硬型电位的情况下推断出新的独特延续结果。
In this paper, we obtain new Carleman estimates for a class of variable coefficient degenerate elliptic operators whose constant coefficient model at one point is the so called Baouendi-Grushin operator. This generalizes the results obtained by the two of us with Garofalo in [9] where similar estimates were established for the "constant coefficient" Baouendi-Grushin operator. Consequently, we obtain: (i) a Bourgain-Kenig type quantitative uniqueness result in the variable coefficient setting; (ii) and a strong unique continuation property for a class of degenerate sublinear equations. We also derive a subelliptic version of a scaling critical Carleman estimate proven by Regbaoui in the Euclidean setting using which we deduce a new unique continuation result in the case of scaling critical Hardy type potentials.
