Grushin型平面上凸函数的比较原理和极大值原理

Comparison and maximum principles for convex functions on Grushin-type planes

目的研究Grushin型平面上凸函数的比较原理和极大值原理。方法利用Null-Lagrangian性质和辅助函数方法。结果给出Grushin型平面上的Monge-Ampère型次椭圆算子和一类线性非散度型次椭圆方程的关于凸函数的比较原理和极大值原理。结论在不具有群结构的Grushin型平面上得到了凸函数的逐点估计性质。

Aim To study the comparison and maximum principles for convex functions on Grushin-type planes. Methods Using Null-Lagrangian property and constructing auxiliary functions. Results The comparison principle of the Monge-Ampere subelliptic operator and maximum principle of the linear nondivergence subelliptic operator are obtained. Conclusion Some properties are given for convex functions on Grushin-type planes.