On a Yamabe Type Problem on Three Dimensional Thin Annulus

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dc.creatorAyed, Mohamed Ben
dc.creatorMehdi, Khalil El
dc.creatorHammami, Mokhless
dc.creatorAhmedou, Mohameden Ould
dc.date2004-08-18
dc.date.accessioned2026-07-07T05:11:21Z
dc.date.available2026-07-07T05:11:21Z
dc.descriptionWe consider a Yamabe type problem on a family $A_ε$ of annulus shaped domains of $\R^3$ which becomes "thin" as $ε$ goes to zero. We show that, for any given positive constant $C$, there exists $ε_0$ such that for any $ε< ε_0$, the problem has no solution $u_ε$ whose energy is less than $C$. Such a result extends to dimension three a result previously known in higher dimensions. Although the strategy to prove this result is the same as in higher dimensions, we need a more careful and delicate blow up analysis of asymptotic profiles of solutions $u_ε$ when $ε$ goes to zero.
dc.description24 pages
dc.identifierhttps://arxiv.org/abs/math/0408238
dc.identifierhttp://arxiv.org/abs/math/0408238
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/72211
dc.subjectAnalysis of PDEs
dc.subject35J65, 58E05, 35B40
dc.titleOn a Yamabe Type Problem on Three Dimensional Thin Annulus
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