By Mahmoudi F., Malchiodi A.
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Additional info for Concentration on minimal submanifolds for a singularly perturbed neumann problem
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The proof follows the same arguments, but for the reader’s convenience we prefer to give details since the notation and the estimates are affected by the different dimensions and codimensions we are dealing with. 5 There exists a small value of the constant C > 0 in (89), depending on Ω, K and p, such that the following property holds. For ε sufficiently small and choosing δ ∈ k2 , k in (89), every function u ∈ HΣε decomposes uniquely as u = u1 + u2 + u3 , u 1 ∈ H 1 , u 2 ∈ H2 , u 3 ∈ H 3 . with Moreover there exists a positive constant C, also depending on Ω, K and p such that 1 (TΣε u3 , u3 ) ≥ CC 33 2 k u3 2 HΣε .
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Concentration on minimal submanifolds for a singularly perturbed neumann problem by Mahmoudi F., Malchiodi A.