Volume 20, Issue 4
Polar Coordinates for the Generalized Baouendi-Grushin Operator and Applications

Jingbo Dou ,  Pengcheng Niu and Junqiang Han

J. Part. Diff. Eq., 20 (2007), pp. 322-336.

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  • 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.

  • History

Published online: 2007-11

  • AMS Subject Headings

35R45, 35J60.

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