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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…