A variational problem for the spatial segregation of reaction-diffusion systems Monica ContiSusanna TerraciniGianmaria Verzini In this paper we study a class of stationary states for reaction-diffusion systems of $k\geq3$ densities having disjoint supports. For a class of segregation states governed by a variational principle we prove existence and provide conditions for uniqueness. Some qualitative properties and the local regularity both of the densities and of their free boundaries are established in the more general context of a functional class characterized by differential inequalities. Indiana University Mathematics Journal 2005 text pdf 10.1512/iumj.2005.54.2506 10.1512/iumj.2005.54.2506 en Indiana Univ. Math. J. 54 (2005) 779 - 816 state-of-the-art mathematics http://iumj.org/access/