Archive for Rational Mechanics and Analysis

, Volume 210, Issue 3, pp 857–908 | Cite as

A Free Boundary Problem Arising from Segregation of Populations with High Competition

  • Veronica Quitalo


In this work, we show how to obtain a free boundary problem as the limit of a fully nonlinear elliptic system of equations that models population segregation of the Gause–Lotka–Volterra type. We study the regularity of the solutions. In particular, we prove Lipschitz regularity across the free boundary. The problem is motivated by the work done by Caffarelli, Karakhanyan and Fang-Hua Lin for the linear case.


Free Boundary Viscosity Solution Lipschitz Domain Comparison Principle Free Boundary Problem 
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© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Department of MathematicsThe University of Texas at AustinAustinUSA

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