Polar Coordinates for the Generalized Baouendi-Grushin Operator and Applications

Authors

  • Jingbo Dou , Pengcheng Niu & Junqiang Han

Keywords:

Generalized Baouendi-Grushin operator;polar coordinate;nonexistence;second order evolution inequality

Abstract

In this parer, by using the polar coordinates for the generalized Baouendi- Grushin operator L_α = \sum^n_{i=1}\frac{∂²}{∂x²_i} + \sum^m_{j=1}|x|^{2α} \frac{∂²}{∂y²_j}, where x = (x_1, x_2, …, x_n) ∈ \mathbb{R}^n, y = (y_1, y_2, …, y_m) ∈ \mathbb{R}^m, α › 0, we obtain the volume of the ball associated to L_α and prove the nonexistence for a second order evolution inequality which is relative to L_α.

Published

2020-05-12

Issue

Section

Articles