| Abstract: |
| We study some qualitative properties of the solutions to a segregation limit problem in planar domains. The main goal is to show that, generically, the limit configuration of \(N\) interacting populations consists of a partition of the domain whose singular points are \(N-2\) triple points, meaning that at most three populations meet at any point on the free boundary. To achieve this, we relate the solutions of the problem to a particular class of harmonic maps in singular spaces, which can be seen as the real part of certain holomorphic functions.The genericity result is obtained by perturbation arguments.
This is a joint work with E. Montefusco, V. Nesi and E. Spadaro (Mathematics Department, Sapienza University, Rome, Italy). |
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