In this article we classify all positive finite energy solutions of the equation −u=u n n−2 |y| in Rn where Rn=Rk ×Rn−k, n>k2 and a point x ∈ Rn is denoted as x=(y, z) ∈ Rk ×Rn−k. As a consequence we obtain the best constant and extremals of a related Hardy–Sobolev inequality.
Mancini, G., Fabbri, I., Sandeep, K. (2006). Classification of solutions of a critical Hardy-Sobolev operator. J. Differential Equations 224 (2006), no. 2, 258--276. JOURNAL OF DIFFERENTIAL EQUATIONS, 224, 258-276-276.
Classification of solutions of a critical Hardy-Sobolev operator. J. Differential Equations 224 (2006), no. 2, 258--276
MANCINI, Giovanni;
2006-01-01
Abstract
In this article we classify all positive finite energy solutions of the equation −u=u n n−2 |y| in Rn where Rn=Rk ×Rn−k, n>k2 and a point x ∈ Rn is denoted as x=(y, z) ∈ Rk ×Rn−k. As a consequence we obtain the best constant and extremals of a related Hardy–Sobolev inequality.File in questo prodotto:
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