Concentration of Solutions for a Singularly Perturbed Neumann Problem in non smooth domains

Abstract

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

24 pages. Second Version, minor changes. To appear in Annales de l'Institut Henri Poincaré - Analyse non linéaire

References in corpus (1)

• Concentration of Solutions for a Singularly Perturbed Neumann Problem in non smooth domains

Cited by in corpus (1)

• Concentration of Solutions for a Singularly Perturbed Neumann Problem in non smooth domains