Calculus of Variations and Geometric Measure Theory

N. Soave - S. Terracini

An anisotropic monotoncity formula, with applications to some segregation problems

created by soave on 16 Mar 2021


Submitted Paper

Inserted: 16 mar 2021
Last Updated: 16 mar 2021

Year: 2020

ArXiv: 2004.08853 PDF


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 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.