Articles

THE HOMOGENEOUS POLYNOMIAL SOLUTIONS FOR THE GRUSHIN OPERATOR

  • Hairong LIU
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  • School of Science, Nanjing Forestry University, Nanjing 210037, China

Received date: 2016-10-29

  Revised date: 2017-11-05

  Online published: 2018-02-25

Supported by

This work is supported by National Natural Science Foundation of China (11401310), Natural Science Foundation of Jiangsu Province (BK20140965), High level talent research fund of Nanjing Forestry University (G2014022), and supported by the overseas research program of Jiangsu Province. The author is sponsored by Qing Lan Project of Jiangsu Province.

Abstract

In this paper, the author computes the dimension of space of homogeneous Grushin-harmonic functions, and give an orthogonal basis of them. Moreover, the author describes the nodal curves of these homogenous Grushin-harmonic basis. As an application of the orthogonal basis, the author proves a Liouville-type theorem for the Grushin operator, that is the Grushin-harmonic functions are homogeneous polynomials provided that the frequency of such a function is equal to some constant.

Cite this article

Hairong LIU . THE HOMOGENEOUS POLYNOMIAL SOLUTIONS FOR THE GRUSHIN OPERATOR[J]. Acta mathematica scientia, Series B, 2018 , 38(1) : 237 -247 . DOI: 10.1016/S0252-9602(17)30129-7

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