ABSTRACT. — We discuss uniqueness and nondegeneracy of extremals for some weighted Sobolev inequalities and give some applications to Grushin and scalar curvature type equations. The main theme is hyperbolic symmetry. KEY WORDS: Nonlinear PDE; hyperbolic symmetry; Hardy–Sobolev inequalities. MATHEMATICS SUBJECT CLASSIFICATION (2000): Primary 35J60; Secondary 35B05, 35A15.
Castorina, D., Fabbri, I., Mancini, G., Sandeep, K. (2008). HARDY-SOBOLEV INEQUALITIES AND HYPERBOLIC SYMMETRY. ATTI DELLA ACCADEMIA NAZIONALE DEI LINCEI. RENDICONTI LINCEI. MATEMATICA E APPLICAZIONI, 19 (2008), NO. 3,, 189-197.