An anisotropic monotonicity formula, with applications to some segregation problems (Q6081865)

Summary: We prove an Alt-Caffarelli-Friedman montonicity formula for pairs of functions solving elliptic equations driven by different ellipticity matrices in their positivity sets. As an application, we derive Liouville-type theorems for subsolutions of some elliptic systems, and we analyze segregation phenomena for systems of equations where the diffusion of each density is described by a different operator.