Di erential Harnack inequalities and Perelman type entropy formulae for subelliptic operators
Di erential Harnack inequalities and Perelman type entropy formulae for subelliptic operators
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亚椭圆算子的微分 Harnack 不等式和 Perelman 型熵公式
DOI：
10.1016/j.na.2017.01.015
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发表时间：
2017
期刊：
影响因子：
--
通讯作者：
Bin Qian
中科院分区：
文献类型：
--
作者：
Bin Qian
在本文中，根据 F. Baudoin 和 N. Garofalo 最近提出的广义曲率维数不等式，我们得到了与势次椭圆算子相关的薛定谔方程的正解的微分 Harnack 不等式（定理 2.1）。作为微分 Harnack 不等式的应用，我们推导出相应的抛物线 Harnack 不等式（定理 4.1）。我们还定义了与亚椭圆算子相关的佩雷尔曼型熵并推导了它的单调性（定理 5.3）。
In this paper, under the generalized curvature-dimension inequality recently intro- duced by F. Baudoin and N. Garofalo, we obtain di erential Harnack inequalities (Theorem 2.1) for the positive solutions to the Schrödinger equation associated to subelliptic operator with potential. As applications of the di erential Harnack inequality, we derive the corresponding parabolic Harnack inequality (Theorem 4.1). Also we de ne the Perelman type entropy associated to subelliptic operators and derive its monotonicity (Theorem 5.3).