JournalsaihpcVol. 27, No. 1pp. 37–56

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

  • Jesus Garcia Azorero

    Departamento de Matemáticas, UAM, 28049 Madrid, Spain

  • Andrea Malchiodi

    SISSA, Via Beirut 2-4, 34014 Trieste, Italy

  • Ireneo Peral

    Departamento de Matemáticas, UAM, 28049 Madrid, Spain

  • Luigi Montoro

    Dipartimento di Matematica, UNICAL, Ponte Pietro Bucci 31 B, 87036 Arcavacata di Rende, Cosenza, Italy
Concentration of solutions for some singularly perturbed mixed problems: Asymptotics of minimal energy solutions cover
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Abstract

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].

Cite this article

Jesus Garcia Azorero, Andrea Malchiodi, Ireneo Peral, Luigi Montoro, Concentration of solutions for some singularly perturbed mixed problems: Asymptotics of minimal energy solutions. Ann. Inst. H. Poincaré Anal. Non Linéaire 27 (2010), no. 1, pp. 37–56

DOI 10.1016/J.ANIHPC.2009.06.005