The homogeneous polynomial solutions for the Grushin operator |
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Authors: | Hairong LIU |
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Institution: | School of Science, Nanjing Forestry University, Nanjing 210037, China |
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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. |
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Keywords: | Grushin operator frequency function homogeneous polynomial 33C45 35C11 35J70 |
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