Concentration phenomena for a fourth order equations with exponential growth: the radial case
| dc.creator | Robert, Frederic | |
| dc.date | 2005-12-07 | |
| dc.date.accessioned | 2026-07-07T06:54:56Z | |
| dc.date.available | 2026-07-07T06:54:56Z | |
| dc.description | We let $Ω$ be a smooth bounded domain of $\mathbb{R}^4$ and a sequence of fonctions $(V_k)_{k\in\mathbb{N}}\in C^0(Ω)$ such that $\lim_{k\to +\infty}V_k=1$ in $C^0_{loc}(Ω)$. We consider a sequence of functions $(u_k)_{k\in\mathbb{N}}\in C^4(Ω)$ such that $$Δ^2 u_k=V_k e^{4u_k}$$ in $Ω$ for all $k\in\mathbb{N}$. We address in this paper the question of the asymptotic behaviour of the $(u_k)'s$ when $k\to +\infty$. The corresponding problem in dimension 2 was considered by Brézis-Merle and Li-Shafrir (among others), where a blow-up phenomenon was described and where a quantization of this blow-up was proved. Surprisingly, as shown by Adimurthi, Struwe and the author, a similar quantization phenomenon does not hold for this fourth order problem. Assuming that the $u_k$'s are radially symmetrical, we push further the previous analysis. We prove that there are exactly three types of blow-up and we describe each type in a very detailed way. | |
| dc.identifier | https://arxiv.org/abs/math/0512149 | |
| dc.identifier | http://arxiv.org/abs/math/0512149 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/106122 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 35B40;35J35 | |
| dc.title | Concentration phenomena for a fourth order equations with exponential growth: the radial case | |
| dc.type | text |