TY - ELEC
AU - Bruno Premoselli
PY - 2019
TI - Compactness of sign-changing solutions to scalar curvature-type equations with bounded negative part.
LA - eng
M3 - Moving Image
AB - We consider the equation $\triangle_g u+hu=|u|^{2^*-2}u$ in a
closed Riemannian manifold $(M,g)$, where $h$ is some Holder continuous
function in $M$ and $2^* = \frac{2n}{n-2}$, $n:=dim M$. We obtain a
sharp compactness result on the sets of sign-changing solutions whose
negative part is a priori bounded. We obtain this result under the
conditions that $n \ge 7$ and $h<(n-2)/(4(n-1)) S_g$ in $M$, where $S_g$
is the Scalar curvature of the manifold. We show that these conditions
are optimal by constructing examples of blowing-up solutions, with
arbitrarily large energy, in the case of the round sphere with a
constant potential function $h$. This is a joint work with J. V\'etois
(McGill University, Montr\'eal)
N2 - We consider the equation $\triangle_g u+hu=|u|^{2^*-2}u$ in a
closed Riemannian manifold $(M,g)$, where $h$ is some Holder continuous
function in $M$ and $2^* = \frac{2n}{n-2}$, $n:=dim M$. We obtain a
sharp compactness result on the sets of sign-changing solutions whose
negative part is a priori bounded. We obtain this result under the
conditions that $n \ge 7$ and $h<(n-2)/(4(n-1)) S_g$ in $M$, where $S_g$
is the Scalar curvature of the manifold. We show that these conditions
are optimal by constructing examples of blowing-up solutions, with
arbitrarily large energy, in the case of the round sphere with a
constant potential function $h$. This is a joint work with J. V\'etois
(McGill University, Montr\'eal)
UR - https://open.library.ubc.ca/collections/48630/items/1.0384913
ER - End of Reference