与广义Baouendi-Grushin算子相关的二阶退化椭圆方程的Hopf型引理

THE HOPF TYPE LEMMA OF DEGENERATE ELLIPTIC EQUATIONS PERTINENT TO THE GENERALIZED BAOUENDI-GRUSHIN OPERATORS

本文研究与广义Baouendi-Grushin(B-G)算子相关的二阶退化椭圆方程.利用广义B-G向量场的拟齐性质建立了相关的拟齐度量,证明了与广义B-G算子相关的退化椭圆方程的Hopf型引理,并给出了有关应用及推广.

This paper investigates degenerate elliptic equations of second order concerning the generalized Baouendi-Grushin operators. By using the quasi-homogeneous properties of the generalized Baouendi-Grushin vector fields the Quasi-distance with regard to them is constructed. Then a Hopf type lemma of the degenerate elliptic equations pertinent to the generalized Baouendi-Grushin operators is proved, application and generalization are also given.