Concentration on minimal submanifolds for a singularly perturbed Neumann problem
| dc.creator | Mahmoudi, Fethi | |
| dc.creator | Malchiodi, Andrea | |
| dc.date | 2006-11-18 | |
| dc.date.accessioned | 2026-07-07T07:33:05Z | |
| dc.date.available | 2026-07-07T07:33:05Z | |
| dc.description | We consider the equation $- \e^2 \D u + u= u^p$ in $Ω\subseteq \R^N$, where $Ω$ is open, smooth and bounded, and we prove concentration of solutions along $k$-dimensional minimal submanifolds of $\partial Ø$, for $N \geq 3$ and for $k \in \{1, ..., N-2\}$. We impose Neumann boundary conditions, assuming $1<p <\frac{N-k+2}{N-k-2}$ and $\e \to 0^+$. This result settles in full generality a phenomenon previously considered only in the particular case $N = 3$ and $k = 1$. | |
| dc.description | 62 pages. To appear in Adv. in Math | |
| dc.identifier | https://arxiv.org/abs/math/0611558 | |
| dc.identifier | http://arxiv.org/abs/math/0611558 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/119334 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 35B25, 35B34, 35J20, 35J60, 53A07 | |
| dc.title | Concentration on minimal submanifolds for a singularly perturbed Neumann problem | |
| dc.type | text |