On a Weiss-type Almost Monotonicity Formula
Analysis of PDEs
2026-04-28 v2
Abstract
We establish a Weiss-type almost-monotonicity formula for a broad class of variable-coefficient energy functionals, assuming only minimal regularity of the coefficients. As an application, we classify blow-up limits for the Alt--Phillips problem with variable coefficients under significantly weaker regularity hypotheses than those imposed in Ara\'ujo et al. [Calc. Var. Partial Differential Equations, 65, no.~1, Paper No.~24 (2026)]. Moreover, by means of a distinct argument, we extend the corresponding free-boundary regularity result. We conclude with a discussion of further extensions, including two-phase analogues.
Cite
@article{arxiv.2604.12712,
title = {On a Weiss-type Almost Monotonicity Formula},
author = {Aelson Sobral},
journal= {arXiv preprint arXiv:2604.12712},
year = {2026}
}