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Concentration of Solutions for Some Singularly Perturbed Neumann Problems

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Geometric Analysis and PDEs

Part of the book series: Lecture Notes in Mathematics ((LNMCIME,volume 1977))

Abstract

The purpose of these notes is to present some techniques for constructing solutions to a class of singularly perturbed problems with a precise asymptotic behavior when the perturbation parameter ε tends to zero. We first treat the case of concentration at points, and then the case of concentration at manifolds. One of the main motivations for the study of these equations arises from reaction-diffusion systems, concerning in particular the so-called Turing’s instability.

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Authors and Affiliations

  1. SISSA, Sector of Mathematical Analysis, Via Beirut 2-4, 34014, Trieste, Italy

    Andrea Malchiodi

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  1. Andrea Malchiodi
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Correspondence to Andrea Malchiodi .

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Editors and Affiliations

  1. Dept. Mathematics, Princeton University, Washington Rd., Princeton, 08544-1000, U.S.A.

    Sun-Yung Alice Chang

  2. Department of Mathematics, SISSA, Via Beirut 2-4, Trieste, 34014, Italy

    Antonio Ambrosetti

  3. Studi Avanzati (SISSA), Scuola Internazionale Superiore di, via Beirut 2-4, Trieste, 34014, Italy

    Andrea Malchiodi

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Malchiodi, A. (2009). Concentration of Solutions for Some Singularly Perturbed Neumann Problems. In: Chang, SY., Ambrosetti, A., Malchiodi, A. (eds) Geometric Analysis and PDEs. Lecture Notes in Mathematics(), vol 1977. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01674-5_3

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