On phase separation in systems of coupled elliptic equations: Asymptotic analysis and geometric aspects

  • Nicola Soave

    Mathematisches Institut, Justus-Liebig-Universität Giessen, Arndtstrasse 2, 35392 Giessen, Germany
  • Alessandro Zilio

    Centre d'Analyse et de Mathématique Sociales, École des Hautes Études en Sciences Sociales, 190-198 Avenue de France, 75244, Paris cedex 13, France

Abstract

We consider a family of positive solutions to the system of components

where with . It is known that uniform bounds in of imply convergence of the densities to a segregated configuration, as the competition parameter diverges to . In this paper we establish sharp quantitative point-wise estimates for the densities around the interface between different components, and we characterize the asymptotic profile of in terms of entire solutions to the limit system

Moreover, we develop a uniform-in- regularity theory for the interfaces.

Cite this article

Nicola Soave, Alessandro Zilio, On phase separation in systems of coupled elliptic equations: Asymptotic analysis and geometric aspects. Ann. Inst. H. Poincaré Anal. Non Linéaire 34 (2017), no. 3, pp. 625–654

DOI 10.1016/J.ANIHPC.2016.04.001