In higher dimensions the free boundary of long-range segregation models has regular parts that are C^1 manifolds of dimension n-1 when singular angles avoid nω_n/2, and convex population supports are convex polytopes.
Quitalo , A free boundary problem arising from segregation of populations with high competition, Arch
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The Free Boundary in a Higher-Dimensional Long-Range Segregation Model
In higher dimensions the free boundary of long-range segregation models has regular parts that are C^1 manifolds of dimension n-1 when singular angles avoid nω_n/2, and convex population supports are convex polytopes.