Concentration on minimal submanifolds for a singularly perturbed Neumann problem |
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Authors: | Fethi Mahmoudi |
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Affiliation: | Sissa, Via Beirut 2-4, 34014 Trieste, Italy |
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Abstract: | We consider the equation −ε2Δu+u=up in Ω⊆RN, 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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Keywords: | 35B25 35B34 35J20 35J60 53A07 |
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