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By Mahmoudi F., Malchiodi A.

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H. Poincar´e Anal. Non Lin´eaire, 22 (2005), 143-163. , Asymptotic behavior and stability of solutions of semilinear diffusion equations, Publ. Res. Inst. Math. Sci. 15 (1979), no. 2, 401-454. , Foliations by constant mean curvature tubes, Communications in Analysis and Geometry, to appear. , Some properties of the eigenfunctions of the Laplace operator on Riemannian manifolds, Canad. J. Math. 1 (1949), 242-256. , Concentration phenomena for solutions of superlinear elliptic problems, Ann. Inst.

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 .

Anal. 82 (1983), no. 4, 347-375. [12] Casten R. , Holland C. , Instability results for reaction diffusion equations with Neumann boundary conditions, J. Diff. Eq. 27 (1978), no. 2, 266-273. , Riemannian geometry, a modern introduction. Cambridge Tracts in Mathematics, 108. Cambridge University Press, Cambridge, 1993. [14] Dancer, E. , Multipeak solutions for a singularly perturbed Neumann problem. Pacific J. Math. 189 (1999), no. 2, 241-262. [15] Dancer, E. , A new type of concentration solutions for a singularly perturbed elliptic problem, preprint.

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Concentration on minimal submanifolds for a singularly perturbed neumann problem by Mahmoudi F., Malchiodi A.

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