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

Jingbo Dou , Pengcheng Niu & Junqiang Han

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

Published online: 2007-11

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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.
  • Keywords

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

  • AMS Subject Headings

35R45 35J60.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JPDE-20-322, author = {Jingbo Dou , Pengcheng Niu and Junqiang Han }, title = {Polar Coordinates for the Generalized Baouendi-Grushin Operator and Applications}, journal = {Journal of Partial Differential Equations}, year = {2007}, volume = {20}, number = {4}, pages = {322--336}, 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.}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5312.html} }
TY - JOUR T1 - Polar Coordinates for the Generalized Baouendi-Grushin Operator and Applications AU - Jingbo Dou , Pengcheng Niu & Junqiang Han 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.
Jingbo Dou , Pengcheng Niu and Junqiang Han . (2007). Polar Coordinates for the Generalized Baouendi-Grushin Operator and Applications. Journal of Partial Differential Equations. 20 (4). 322-336. doi:
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