TY - JOUR
T1 - Polar Coordinates for the Generalized Baouendi-Grushin Operator and Applications
JO - Journal of Partial Differential Equations
VL - 4
SP - 322
EP - 336
PY - 2007
DA - 2007/11
SN - 20
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jpde/5312.html
KW - Generalized Baouendi-Grushin operator
KW - polar coordinate
KW - nonexistence
KW - second order evolution inequality
AB -  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.