Concentration on minimal submanifolds for a singularly perturbed Neumann problem

dc.creatorMahmoudi, Fethi
dc.creatorMalchiodi, Andrea
dc.date2006-11-18
dc.date.accessioned2026-07-07T07:33:05Z
dc.date.available2026-07-07T07:33:05Z
dc.descriptionWe 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.description62 pages. To appear in Adv. in Math
dc.identifierhttps://arxiv.org/abs/math/0611558
dc.identifierhttp://arxiv.org/abs/math/0611558
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/119334
dc.subjectAnalysis of PDEs
dc.subject35B25, 35B34, 35J20, 35J60, 53A07
dc.titleConcentration on minimal submanifolds for a singularly perturbed Neumann problem
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