Concentration on minimal submanifolds for a singularly perturbed Neumann problem

Fethi Mahmoudi, Andrea Malchiodi

We consider the equation $- \e^2 \D u + u= u^p$ in $\Omega \subseteq {\mathbb{R}}^N$, where $\Omega$ is open, smooth and bounded, and we prove concentration of solutions along $k$-dimensional minimal s…