An anisotropic monotonicity formula, with applications to some segregation problems
Nicola Soave
Politecnico di Milano, ItalySusanna Terracini
Università degli studi di Torino, Italy
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Abstract
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.
Cite this article
Nicola Soave, Susanna Terracini, An anisotropic monotonicity formula, with applications to some segregation problems. J. Eur. Math. Soc. 25 (2023), no. 9, pp. 3727–3765
DOI 10.4171/JEMS/1270