Non UBC
DSpace
Bruno Premoselli
2019-11-04T09:53:54Z
2019-05-07T16:44
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)
https://circle.library.ubc.ca/rest/handle/2429/72179?expand=metadata
40.0 minutes
video/mp4
Author affiliation: Université Libre de Bruxelles
Banff (Alta.)
10.14288/1.0384913
eng
Unreviewed
Vancouver : University of British Columbia Library
Banff International Research Station for Mathematical Innovation and Discovery
Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
Researcher
BIRS Workshop Lecture Videos (Banff, Alta)
Mathematics
Partial differential equations
Differential geometry
Compactness of sign-changing solutions to scalar curvature-type equations with bounded negative part.
Moving Image
http://hdl.handle.net/2429/72179