We consider the equation \( - \e^2 \D u + u = u^p \) in \( \O \subseteq \R^N \), where \( \O \) is open, smooth and bounded, and we prove concentration of solutions along -dimensional minimal submanifolds of \( \pa \O \), for and for . We impose Neumann boundary conditions, assuming and \( \e \to 0^+ \). This result settles in full generality a phenomenon previously considered only in the particular case and .
Cite this article
Andrea Malchiodi, Fethi Mahmoudi, Concentration at manifolds of arbitrary dimension for a singularly perturbed Neumann problem. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 17 (2006), no. 3, pp. 279–290DOI 10.4171/RLM/469