A self-contained proof of the Alt-Caffarelli-Friedman monotonicity formula
arXiv:2506.13473
Abstract
The Alt-Caffarelli-Friedman monotonicity formula is a cornerstone in the theory of free boundary problems. In this note we provide a self-contained proof of this result. To prove the main stepping stone, namely the Friedland-Hayman inequality, we exploit a useful convexity property.