Annales Mathématiques
Blaise Pascal
no. 1
The second Yamabe invariant with singularities
Mohammed Benalili1 ; Hichem Boughazi1
1 Université Aboubekr Belkaïd Faculty of Sciences Dept. of Math. B.P. 119 Tlemcen, Algeria
Annales mathématiques Blaise Pascal, Tome 19 (2012) no. 1, pp. 147-176.

Let (M,g) be a compact Riemannian manifold of dimension n≥3.We suppose that g is a metric in the Sobolev space H 2 p (M,T * M⊗T * M) with p>n 2 and there exist a point P∈M and δ>0 such that g is smooth in the ball B p (δ). We define the second Yamabe invariant with singularities as the infimum of the second eigenvalue of the singular Yamabe operator over a generalized class of conformal metrics to g and of volume 1. We show that this operator is attained by a generalized metric, we deduce nodal solutions to a Yamabe type equation with singularities.

DOI : 10.5802/ambp.308
Classification : 58J05
Mots clés : Second Yamabe invariant, singularities, Critical Sobolev growth.

Mohammed Benalili 1 ; Hichem Boughazi 1

1 Université Aboubekr Belkaïd Faculty of Sciences Dept. of Math. B.P. 119 Tlemcen, Algeria 
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Mohammed Benalili; Hichem Boughazi. The second Yamabe invariant with singularities. Annales mathématiques Blaise Pascal, Tome 19 (2012) no. 1, pp. 147-176. doi : 10.5802/ambp.308. https://ambp.centre-mersenne.org/articles/10.5802/ambp.308/

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