par Cheikh-Ali, Hussein
Référence Pacific journal of mathematics, 316, 2, page (249-276)
Publication Publié, 2022-02
Article révisé par les pairs
Résumé : We consider the second best constant in the Hardy-Sobolev inequality on a Riemannian manifold. More precisely, we are interested in the existence of extremal functions for this inequality. This problem was tackled by Djadli and Druet (Calc. Var. Partial Differential Equations 12 (2001), 59-84) for Sobolev inequalities. Here, we establish the corresponding result for the singular case. In addition, we perform a blow-up analysis of solutions to Hardy-Sobolev equations of minimizing type. This yields information on the value of the second best constant in the related Riemannian functional inequality.

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