Concentration on minimal submanifolds for a singularly perturbed Neumann problem

Details Concentration on minimal submanifolds for a singularly perturbed Neumann problem Concentration on minimal submanifolds for a singularly perturbed Neumann problem

2006-11-18

arxiv.org/abs/math/0611558v1

Mathematics

Analysis of PDEs

62 pages. To appear in Adv. in Math

Scientific paper

We consider the equation $- \e^2 \D u + u= u^p$ in $\Omega \subseteq \R^N$, where $\Omega$ is open, smooth and bounded, and we prove concentration of solutions along $k$-dimensional minimal submanifolds of $\partial \O$, for $N \geq 3$ and for $k \in \{1, ..., N-2\}$. We impose Neumann boundary conditions, assuming $1

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