On a class of Nonlinear Grushin equations
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912839086637056 |
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| author | Bauer, Wolfram Wei, Yawei Zhou, Xiaodong |
| author_facet | Bauer, Wolfram Wei, Yawei Zhou, Xiaodong |
| contents | In this paper, we study two kinds of nonlinear degenerate elliptic equations containing the Grushin operator. First, we prove radial symmetry and a decay rate at infinity of solutions to such a Grushin equation by using the moving plane method in combination with suitable integral inequalities. Applying similar methods, we obtain nonexistence results for solutions to a second type of Grushin equation in Euclidean half space. Finally, we derive a priori estimates and the existence for positive solutions to more general types of Grushin equations by employing blow up analysis and topological degree methods, respectively. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_08039 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On a class of Nonlinear Grushin equations Bauer, Wolfram Wei, Yawei Zhou, Xiaodong Analysis of PDEs 35J70, 35B45, 35A16 In this paper, we study two kinds of nonlinear degenerate elliptic equations containing the Grushin operator. First, we prove radial symmetry and a decay rate at infinity of solutions to such a Grushin equation by using the moving plane method in combination with suitable integral inequalities. Applying similar methods, we obtain nonexistence results for solutions to a second type of Grushin equation in Euclidean half space. Finally, we derive a priori estimates and the existence for positive solutions to more general types of Grushin equations by employing blow up analysis and topological degree methods, respectively. |
| title | On a class of Nonlinear Grushin equations |
| topic | Analysis of PDEs 35J70, 35B45, 35A16 |
| url | https://arxiv.org/abs/2412.08039 |