Uniqueness and least energy property for solutions to strongly competing systems
Monica Conti
Politecnico, Milano, ItalySusanna Terracini
Università di Torino, ItalyGianmaria Verzini
Politecnico di Milano, Italy

Abstract
For the reaction--diffusion system of three competing species:
\[ -\D u_i=-\kappa u_i\sum_{j\neq i}u_j,\qquad i=1,2,3, \]we prove uniqueness of the limiting configuration as on a planar domain \( \O \), with appropriate boundary conditions. Moreover we prove that the limiting configuration minimizes the energy associated to the system
\[ E(U)=\sum_{i=1}^3\int_\O|\nabla u_i(\bx)|^2\,d\bx \]among all segregated states ( a.e.) with the same boundary conditions.
Cite this article
Monica Conti, Susanna Terracini, Gianmaria Verzini, Uniqueness and least energy property for solutions to strongly competing systems. Interfaces Free Bound. 8 (2006), no. 4, pp. 437–446
DOI 10.4171/IFB/150