# The second Yamabe invariant with singularities

Mohammed Benalili^{[1]}; Hichem Boughazi^{[1]}

- [1] Université Aboubekr Belkaïd Faculty of Sciences Dept. of Math. B.P. 119 Tlemcen, Algeria

Annales mathématiques Blaise Pascal (2012)

- Volume: 19, Issue: 1, page 147-176
- ISSN: 1259-1734

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topBenalili, Mohammed, and Boughazi, Hichem. "The second Yamabe invariant with singularities." Annales mathématiques Blaise Pascal 19.1 (2012): 147-176. <http://eudml.org/doc/251055>.

@article{Benalili2012,

abstract = {Let $(M,g)$ be a compact Riemannian manifold of dimension $n\ge 3$.We suppose that $ g$ is a metric in the Sobolev space $H_\{2\}^\{p\}(M,T^\{\ast \}M\otimes T^\{\ast \}M)$ with $ p>\frac\{n\}\{2\}$ and there exist a point $\ P\in M$ and $ \delta >0$ such that $g$ is smooth in the ball $\ B_\{p\}(\delta )$. 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.},

affiliation = {Université Aboubekr Belkaïd Faculty of Sciences Dept. of Math. B.P. 119 Tlemcen, Algeria; Université Aboubekr Belkaïd Faculty of Sciences Dept. of Math. B.P. 119 Tlemcen, Algeria},

author = {Benalili, Mohammed, Boughazi, Hichem},

journal = {Annales mathématiques Blaise Pascal},

keywords = {Second Yamabe invariant; singularities; Critical Sobolev growth; second Yamabe invariant; critical Sobolev growth},

language = {eng},

month = {1},

number = {1},

pages = {147-176},

publisher = {Annales mathématiques Blaise Pascal},

title = {The second Yamabe invariant with singularities},

url = {http://eudml.org/doc/251055},

volume = {19},

year = {2012},

}

TY - JOUR

AU - Benalili, Mohammed

AU - Boughazi, Hichem

TI - The second Yamabe invariant with singularities

JO - Annales mathématiques Blaise Pascal

DA - 2012/1//

PB - Annales mathématiques Blaise Pascal

VL - 19

IS - 1

SP - 147

EP - 176

AB - Let $(M,g)$ be a compact Riemannian manifold of dimension $n\ge 3$.We suppose that $ g$ is a metric in the Sobolev space $H_{2}^{p}(M,T^{\ast }M\otimes T^{\ast }M)$ with $ p>\frac{n}{2}$ and there exist a point $\ P\in M$ and $ \delta >0$ such that $g$ is smooth in the ball $\ B_{p}(\delta )$. 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.

LA - eng

KW - Second Yamabe invariant; singularities; Critical Sobolev growth; second Yamabe invariant; critical Sobolev growth

UR - http://eudml.org/doc/251055

ER -

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