A system with weights and with critical Sobolev exponent
Résumé
In this paper, we investigate the minimization problem : inf u ∈ H 1 0 (Ω), v ∈ H 1 0 (Ω), u L q = 1, v L q = 1 1 2 Ω a(x)|∇u(x)| 2 dx + 1 2 Ω b(x)|∇v(x)| 2 dxλ Ω u(x)v(x)dx where q = 2N N-2 , N ≥ 4, a and b are two continuous positive weight functions. We show the existence of solutions of the previous minimizing problem under some conditions on a, b, the dimension of the space and the parameter λ.
Domaines
Mathématiques [math]
Origine : Fichiers produits par l'(les) auteur(s)