Concentration on minimal submanifolds for a singularly perturbed Neumann problem
نویسنده
چکیده
We consider the equation −ε2∆u+u = u in Ω ⊆ R , where Ω is open, smooth and bounded, and we prove concentration of solutions along k-dimensional minimal submanifolds of ∂Ω, for N ≥ 3 and for k ∈ {1, . . . , N − 2}. We impose Neumann boundary conditions, assuming 1 < p < N−k+2 N−k−2 and ε → 0+. This result settles in full generality a phenomenon previously considered only in the particular case N = 3 and k = 1.
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