Concentration at curves for a singularly perturbed Neumann problem in three-dimensional domains

Abstract.

We prove new concentration phenomena for the equation −ɛ² Δu + u = u ^p in a smooth bounded domain $\Omega \subseteq \mathbb{R}^3$ and with Neumann boundary conditions. Here p > 1 and ɛ > 0 is small. We show that concentration of solutions occurs at some geodesics of ∂Ω when ɛ → 0.