Concentration of solutions for a singularly perturbed Neumann problem in non-smooth domains

Dipierro, Serena

Annales de l'I.H.P. Analyse non linéaire, Tome 28 (2011) no. 1, pp. 107-126.

We consider the equation $-{ϵ}^2\Delta u+u=u^p$ in a bounded domain $\Omega \subset {ℝ}^3$ with edges. We impose Neumann boundary conditions, assuming $1<p<5$, and prove concentration of solutions at suitable points of ∂Ω on the edges.

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