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arXiv · 2412.08039

On a class of Nonlinear Grushin equations

Wolfram Bauer·Yawei Wei·Xiaodong Zhou
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Abstract

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.

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Wolfram Bauer, Yawei Wei, Xiaodong Zhou. 2024-12-11. On a class of Nonlinear Grushin equations. https://arxiv.org/abs/2412.08039

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