WIAS Preprint No. 2137, (2015)

On a long range segregation model


  • Caffarelli, Luis
  • Patrizi, Stefania
  • Quitalo, Veronica

2010 Mathematics Subject Classification

  • 35J60 35R35 35B65 35Q92


  • regularity for viscosity solutions, segregation of populations




Segregation phenomena occurs in many areas of mathematics and science: from equipartition problems in geometry, to social and biological processes (cells, bacteria, ants, mammals) to finance (sellers and buyers). There is a large body of literature studying segregation models where the interaction between species is punctual. There are many processes though, where the growth of a population at a point is inhibited by the populations in a full area surrounding that point. This work is a first attempt to study the properties of such a segregation process.

Appeared in

  • J. Eur. Math. Soc., 19 (2017), pp. 3575-3628.

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