Liouville Theorem for Lane Emden Equation of Baouendi Grushin operators
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909383103873024 |
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| author | Liao, Xin Chen, Hua |
| author_facet | Liao, Xin Chen, Hua |
| contents | In this paper, we establish a Liouville theorem for solutions to the Lane Emden equation involving Baouendi Grushin operators. We focus on solutions that are stable outside a compact set. Specifically, we prove that when p is smaller than the Joseph Lundgren exponent and differs from the Sobolev exponent, 0 is the unique solution stable outside a compact set. This work extends the results obtained by Farina (J. Math. Pures Appl., 87 (5) (2007)). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_06354 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Liouville Theorem for Lane Emden Equation of Baouendi Grushin operators Liao, Xin Chen, Hua Analysis of PDEs In this paper, we establish a Liouville theorem for solutions to the Lane Emden equation involving Baouendi Grushin operators. We focus on solutions that are stable outside a compact set. Specifically, we prove that when p is smaller than the Joseph Lundgren exponent and differs from the Sobolev exponent, 0 is the unique solution stable outside a compact set. This work extends the results obtained by Farina (J. Math. Pures Appl., 87 (5) (2007)). |
| title | Liouville Theorem for Lane Emden Equation of Baouendi Grushin operators |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2411.06354 |