The second Yamabe invariant with singularities

Benalili, 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&gt;\frac\{n\}\{2\}$ and there exist a point $\ P\in M$ and $ \delta &gt;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&gt;\frac{n}{2}$ and there exist a point $\ P\in M$ and $ \delta &gt;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 -