A Sobolev-Hardy Inequality with¶Applications to a Nonlinear Elliptic Equation¶arising in Astrophysics

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On horizontal Hardy, Rellich, Caffarelli–Kohn–Nirenberg and p-sub-Laplacian inequalities on stratified groups (2016, methodology): “Moreover, a new simple proof of the Badiale-Tarantello conjecture [2] on the best constant of a Hardy type inequality is provided.”
Existence and non-existence of solutions to elliptic equations related to the Caffarelli–Kohn–Nirenberg inequalities (2007, background): “Moreover, some interesting results such as the existence and non-existence of the extremal functions and the symmetry and non-symmetry of the extremal functions were discussed; see [3, 9, 16, 28, 30, 34, 35], for instance.”
Partial symmetry and asymptotic behavior for some elliptic variational problems (2003, background): “2 can be proved in many different nearby settings, like invariance under subgroups of SO(N ) as cylindrical symmetry in [ 2 ].”
On a semilinear elliptic equation in Hn (2008, methodology): “results extend (in case k6= 2) a result in [ 5 ], where k > 1 and = 0.”
Hardy–Sobolev extremals, hyperbolic symmetry and scalar curvature equations (2009, unknown): “4) (see [5,6] and [24]) due to invariance properties of (1.”