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arXiv · 2604.12712

On a Weiss-type Almost Monotonicity Formula

Aelson Sobral
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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.

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Aelson Sobral. 2026-04-14. On a Weiss-type Almost Monotonicity Formula. https://arxiv.org/abs/2604.12712

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