3 papers
math.AP2025
On a fractional Alt-Caffarelli-Friedman-type monotonicity formula
Fausto Ferrari, Davide Giovagnoli, Enzo Maria Merlino
In this note, by exploiting mean value properties of -harmonic functions, we introduce some monotonicity formulas in the nonlocal setting. We take into account intrinsically non…
math.AP2025
On the Geometry of Solutions of the Fully Nonlinear Inhomogeneous One-Phase Stefan Problem
Fausto Ferrari, Davide Giovagnoli, David Jesus
In this paper, we characterize the geometry of solutions to one-phase inhomogeneous fully nonlinear Stefan problem with flat free boundaries under a new nondegeneracy assumption. T…
math.AP2024
Some counterexamples to Alt-Caffarelli-Friedman monotonicity formulas in Carnot groups
Fausto Ferrari, Davide Giovagnoli
In this paper we continue the analysis of an Alt-Caffarelli-Friedman (ACF) monotonicity formula in Carnot groups of step confirming the existence of counterexamples to the m…