Quantization effects for a fourth order equation of exponential growth in dimension four
| 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 investigate the asymptotic behavior as $k \to +\infty$ of sequences $(u_k)_{k\in\mathbb{N}}\in C^4(Ω)$ of solutions of the equations $Δ^2 u_k=V_k e^{4u_k}$ on $Ω$, where $Ω$ is a bounded domain of $\mathbb{R}^4$ and $\lim_{k\to +\infty}V_k=1$ in $C^0_{loc}(Ω)$. The corresponding 2-dimensional problem was studied by Brézis-Merle and Li-Shafrir who pointed out that there is a quantization of the energy when blow-up occurs. As shown by Adimurthi, Struwe and the author, such a quantization does not hold in dimension four for the problem in its full generality. We prove here that under natural hypothesis on $Δu_k$, we recover such a quantization as in dimension 2. | |
| dc.identifier | https://arxiv.org/abs/math/0512148 | |
| dc.identifier | http://arxiv.org/abs/math/0512148 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/106121 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 35B40;35J35 | |
| dc.title | Quantization effects for a fourth order equation of exponential growth in dimension four | |
| dc.type | text |