On a class of Nonlinear Grushin equations
Analysis of PDEs
2026-01-23 v2
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.
Cite
@article{arxiv.2412.08039,
title = {On a class of Nonlinear Grushin equations},
author = {Wolfram Bauer and Yawei Wei and Xiaodong Zhou},
journal= {arXiv preprint arXiv:2412.08039},
year = {2026}
}