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Hardy-Sobolev inequalities and hyperbolic symmetry. (English) Zbl 1194.35146

Summary: We discuss uniqueness and nondegeneracy of extremals for some wheighted Sobolev inequalities and give some applications to Grushin and scalar curvature type equations. The main theme is hyperbolic symmetry.

MSC:

35J60 Nonlinear elliptic equations
35A25 Other special methods applied to PDEs
35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
35A15 Variational methods applied to PDEs
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