Benvenuti nell'Anagrafe della Ricerca d'Ateneo
La valutazione delle attività di ricerca che si svolgono nelle università ha assunto un'importanza rilevante sia per l'intero sistema universitario sia all'interno di ogni singolo ateneo. Roma Tre si è quindi dotata di idonei strumenti informativi in grado di supportare al meglio le azioni di monitoraggio e di valutazione delle attività di ricerca svolte nei propri dipartimentied ha realizzato una Anagrafe della Ricerca di Ateneo.
EnglishLet (M,g) be a smooth, compact Riemannian manifold of dimension N \geq 3. We consider the almost critical problem (P_\epsilon) -\Delta_g u+ {N-2\over 4(N-1)} Scal_g u= u^{{N+2\over N-2}+\epsilon } in} M, u>0 in M, where \Delta_g denotes the Laplace-Beltrami operator, Scal_g is the scalar curvature of g and \epsilon \in R is a small parameter. It is known that problem (P_\epsilon) does not have any blowing-up solutions when \epsilon \to 0^-, at least for N \leq 24 or in the locally conformally flat case, and this is not true anymore when \epsilon \to 0^+. Indeed, we prove that, if N \geq 7 and the manifold is not locally conformally flat, then problem (P_\epsilon) does have a family of solutions which blow-up at a maximum point of the function \xi \to |Weyl_g(\xi)|_g as \epsilon \to 0^+. Here Weyl_g denotes the Weyl curvature tensor of g.
ESPOSITO P, & PISTOIA A (2014). Blowing-up solutions for the Yamabe equation. PORTUGALIAE MATHEMATICA, 71(3-4), 249-276.
| Titolo: | Blowing-up solutions for the Yamabe equation |
| Autori: | |
| Data di pubblicazione: | 2014 |
| Rivista: | |
| Citazione: | ESPOSITO P, & PISTOIA A (2014). Blowing-up solutions for the Yamabe equation. PORTUGALIAE MATHEMATICA, 71(3-4), 249-276. |
| Abstract: | Let (M,g) be a smooth, compact Riemannian manifold of dimension N \geq 3. We consider the almost critical problem (P_\epsilon) -\Delta_g u+ {N-2\over 4(N-1)} Scal_g u= u^{{N+2\over N-2}+\epsilon } in} M, u>0 in M, where \Delta_g denotes the Laplace-Beltrami operator, Scal_g is the scalar curvature of g and \epsilon \in R is a small parameter. It is known that problem (P_\epsilon) does not have any blowing-up solutions when \epsilon \to 0^-, at least for N \leq 24 or in the locally conformally flat case, and this is not true anymore when \epsilon \to 0^+. Indeed, we prove that, if N \geq 7 and the manifold is not locally conformally flat, then problem (P_\epsilon) does have a family of solutions which blow-up at a maximum point of the function \xi \to |Weyl_g(\xi)|_g as \epsilon \to 0^+. Here Weyl_g denotes the Weyl curvature tensor of g. |
| Handle: | http://hdl.handle.net/11590/140811 |
| Appare nelle tipologie: | 1.1 Articolo in rivista |
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