The second Yamabe invariant with singularities
Annales Mathématiques Blaise Pascal, Tome 19 (2012) no. 1, pp. 147-176.

Let (M,g) be a compact Riemannian manifold of dimension n3.We suppose that g is a metric in the Sobolev space H 2 p (M,T * MT * M) with p>n 2 and there exist a point PM 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 : https://doi.org/10.5802/ambp.308
Classification : 58J05
Mots clés: Second Yamabe invariant, singularities, Critical Sobolev growth.
@article{AMBP_2012__19_1_147_0,
     author = {Mohammed Benalili and Hichem Boughazi},
     title = {The second Yamabe invariant with singularities},
     journal = {Annales Math\'ematiques Blaise Pascal},
     pages = {147--176},
     publisher = {Annales math\'ematiques Blaise Pascal},
     volume = {19},
     number = {1},
     year = {2012},
     doi = {10.5802/ambp.308},
     mrnumber = {2978317},
     zbl = {1256.58005},
     language = {en},
     url = {ambp.centre-mersenne.org/item/AMBP_2012__19_1_147_0/}
}
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/item/AMBP_2012__19_1_147_0/

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