Concentration of solutions for some singularly perturbed mixed problems: Asymptotics of minimal energy solutions

Garcia Azorero, Jesus; Malchiodi, Andrea; Montoro, Luigi; Peral, Ireneo

Annales de l'I.H.P. Analyse non linéaire, Tome 27 (2010) no. 1, pp. 37-56.

In this paper we carry on the study of asymptotic behavior of some solutions to a singularly perturbed problem with mixed Dirichlet and Neumann boundary conditions, started in the first paper [J. Garcia Azorero, A. Malchiodi, L. Montoro, I. Peral, Concentration of solutions for some singularly perturbed mixed problems: Existence results, Arch. Ration. Mech. Anal., in press]. Here we are mainly interested in the analysis of the location and shape of least energy solutions when the singular perturbation parameter tends to zero. We show that in many cases they coincide with the new solutions produced in [J. Garcia Azorero, A. Malchiodi, L. Montoro, I. Peral, Concentration of solutions for some singularly perturbed mixed problems: Existence results, Arch. Ration. Mech. Anal., in press].

Classification : 35B25, 35B34, 35J20, 35J60
Mots clés : Singularly perturbed elliptic problems, Finite-dimensional reductions, Local inversion

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