Kelvin transform for Grushin operators and critical semilinear equations

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Sobolev Inequalities for Weighted Gradients (2006, methodology): “In Monti and Morbidelli (2006), any positive function u ∈ C2 n solving equation (1.2) is proved to be of the form (1.3), up to translation in the variable y and scaling u x y = Q−22 u x +1y for some positive number .”
Attractors for a class of semi-linear degenerate parabolic equations (2013, background): “, [15], where the subelliptic equation with critical nonlinearities was considered, and the references therein.”
On a semilinear elliptic equation in Hn (2008, background): “previous results by Garofalo-Vassilev on Yamabe-type equations on groups of Heisenberg type [11], Monti and Morbidelli [18] enlightened the role of hyperbolic symmetry built in Grushin-type equations.”
Maximum principles and the method of moving planes for a class of degenerate elliptic linear operators (2010, methodology): “In the paper of Monti–Morbidelli [20] it is also shown that any solution of problem (2) with p = (Q+ 2)/(Q− 2) must exhibit a kind of ”spherical symmetry”, by exploiting the invariance of the equation with respect to a suitable conformal inversion, i.”
Hardy–Sobolev extremals, hyperbolic symmetry and scalar curvature equations (2009, unknown): “4) is also related to critical Grushin-type equations (see [22] for related uniqueness results).”