David Jesus

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20242026

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math.AP2025

$C^{1 + α}$ regularity for fractional $p$ -harmonic functions

Davide Giovagnoli, David Jesus, Luis Silvestre

We establish interior $C^{1, α}$ regularity estimates for some $α > 0$ , for solutions of the fractional $p$ -Laplace equation $(- Δ_{p})^{s} u = 0$ when $p$ is in the range $p \in [2,2/(1-…

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…

C1+α regularity for fractional p-harmonic functions

On the Geometry of Solutions of the Fully Nonlinear Inhomogeneous One-Phase Stefan Problem

$C^{1 + α}$ regularity for fractional $p$ -harmonic functions