A self-contained proof of the Alt-Caffarelli-Friedman monotonicity formula
Analysis of PDEs
2026-05-22 v2
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.
Keywords
Cite
@article{arxiv.2506.13473,
title = {A self-contained proof of the Alt-Caffarelli-Friedman monotonicity formula},
author = {Emanuele Salato},
journal= {arXiv preprint arXiv:2506.13473},
year = {2026}
}