We prove new concentration phenomena for the equation −ɛ2 Δu + u = u p in a smooth bounded domain Ω⊆R3 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.
Concentration at curves for a singularly perturbed Neumann problem in three-dimensional domains
Malchiodi, Andrea
2005
Abstract
We prove new concentration phenomena for the equation −ɛ2 Δu + u = u p in a smooth bounded domain Ω⊆R3 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.File in questo prodotto:
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