"Non UBC"@en .
"DSpace"@en .
"Bruno Premoselli"@en .
"2019-11-04T09:53:54Z"@en .
"2019-05-07T16:44"@en .
"We consider the equation $\triangle_g u+hu=|u|^{2^*-2}u$ in a \nclosed Riemannian manifold $(M,g)$, where $h$ is some Holder continuous \nfunction in $M$ and $2^* = \frac{2n}{n-2}$, $n:=dim M$. We obtain a \nsharp compactness result on the sets of sign-changing solutions whose \nnegative part is a priori bounded. We obtain this result under the \nconditions that $n \ge 7$ and $h<(n-2)/(4(n-1)) S_g$ in $M$, where $S_g$ \nis the Scalar curvature of the manifold. We show that these conditions \nare optimal by constructing examples of blowing-up solutions, with \narbitrarily large energy, in the case of the round sphere with a \nconstant potential function $h$. This is a joint work with J. V\'etois \n(McGill University, Montr\'eal)"@en .
"https://circle.library.ubc.ca/rest/handle/2429/72179?expand=metadata"@en .
"40.0 minutes"@en .
"video/mp4"@en .
""@en .
"Author affiliation: Universit\u00E9 Libre de Bruxelles"@en .
"Banff (Alta.)"@en .
"10.14288/1.0384913"@en .
"eng"@en .
"Unreviewed"@en .
"Vancouver : University of British Columbia Library"@en .
"Banff International Research Station for Mathematical Innovation and Discovery"@en .
"Attribution-NonCommercial-NoDerivatives 4.0 International"@en .
"http://creativecommons.org/licenses/by-nc-nd/4.0/"@en .
"Researcher"@en .
"BIRS Workshop Lecture Videos (Banff, Alta)"@en .
"Mathematics"@en .
"Partial differential equations"@en .
"Differential geometry"@en .
"Compactness of sign-changing solutions to scalar curvature-type equations with bounded negative part."@en .
"Moving Image"@en .
"http://hdl.handle.net/2429/72179"@en .