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Concentration on minimal submanifolds for a singularly perturbed Neumann problem

TitleConcentration on minimal submanifolds for a singularly perturbed Neumann problem
Publication TypeJournal Article
Year of Publication2007
AuthorsMahmoudi, F, Malchiodi, A
JournalAdv. Math. 209 (2007) 460-525
Abstract

We consider the equation $- \\\\e^2 \\\\D u + u= u^p$ in $\\\\Omega \\\\subseteq \\\\R^N$, where $\\\\Omega$ is open, smooth and bounded, and we prove concentration of solutions along $k$-dimensional minimal submanifolds of $\\\\partial \\\\O$, for $N \\\\geq 3$ and for $k \\\\in \\\\{1, ..., N-2\\\\}$. We impose Neumann boundary conditions, assuming $1

URLhttp://hdl.handle.net/1963/2013
DOI10.1016/j.aim.2006.05.014

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