JournalsaihpcVol. 28, No. 1pp. 107–126

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

  • Serena Dipierro

    SISSA, Sector of Mathematical Analysis, Via Bonomea 265, 34136 Trieste, Italy
Concentration of solutions for a singularly perturbed Neumann problem in non-smooth domains cover
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Abstract

We consider the equation ϵ2Δu+u=up−\epsilon ^{2}\mathrm{\Delta }u + u = u^{p} in a bounded domain ΩR3\Omega \subset \mathbb{R}^{3} with edges. We impose Neumann boundary conditions, assuming 1<p<51 < p < 5, and prove concentration of solutions at suitable points of ∂Ω on the edges.

Cite this article

Serena Dipierro, Concentration of solutions for a singularly perturbed Neumann problem in non-smooth domains. Ann. Inst. H. Poincaré Anal. Non Linéaire 28 (2011), no. 1, pp. 107–126

DOI 10.1016/J.ANIHPC.2010.11.003