一类Baouendi-Grushin方程解的对称性

The symmetry of solutions for a class of Baouendi-Grushin equations

研究一类Baouendi-Grushin方程解的对称性问题。将该方程解的对称性转化为一类带约束条件的极小化泛函问题,再通过Sobolev嵌入定理及解的先验估计,证明了Schwarz重排后的解也是其拉格朗日极小化泛函的解。从而得到了Baouendi-Grushin方程解的存在性和对称性。

To study the symmetry for solutions of a class of Baouendi-Grushin equations,first the symmetry is converted into a constrained minimization problem.Then,by Sobolev embedding theorem and some priori estimates, it is proved that the solutions after Schwarz rearrangement are also the solutions of its Lagrangian minimization functional.Thus the existence and symmetry results of the solutions of Baouendi-Grushin equations.