Minimal Coexistence Configurations for Multispecies Systems

  title={Minimal Coexistence Configurations for Multispecies Systems},
  author={Veronica Felli},
We deal with strongly competing multispecies systems of Lotka-Volterra type with homogeneous Neumann boundary conditions in dumbbell-like domains. Under suitable non-degeneracy assumptions, we show that, as the competition rate grows indefinitely, the system reaches a state of coexistence of all the species in spatial segregation. Furthermore, the limit configuration is a local minimizer for the associated free energy. 

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