(untitled) (Journal of Partial Differential Equations, 2020)
In this parer, by using the polar coordinates for the generalized Baouendi- Grushin operator L_α = ^n_i=1∂²∂x²_i + ^m_j=1|x|^2α ∂²∂y²_j, where x = (x_1, x_2, …, x_n) ∈ R^n, y = (y_1, y_2, …, y_m) ∈ 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.