David Jesus

activity

20242026

collaborators

6 papers

math.AP2026

Hölder gradient estimates for fractional $p$ -caloric functions

Davide Giovagnoli, David Jesus, Luis Silvestre

We establish interior $C^{1, α}$ regularity estimates, for some $α > 0$ , for fractional $p$ -caloric functions when $p$ is in the range $p \in (2, 2/ (1 - s))$ . As a consequence, we deduc…

math.AP2026

A transmission problem arising from the two-phase Stefan problem

Fausto Ferrari, Davide Giovagnoli, David Jesus

We study a parabolic transmission problem whose interface condition depends on the time derivative of the solution. This model arises naturally as the linearized limiting profile o…

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…

math.AP2024

A fully nonlinear transmission problem degenerating on the interface

Davide Giovagnoli, David Jesus

In this paper we prove that solutions to a transmission problem degenerating on the interface are Hölder differentiable up to the interface with universal estimates. Furthermore, w…

math.AP2024

Free boundary regularity for the inhomogeneous one-phase Stefan problem

Fausto Ferrari, Nicolò Forcillo, Davide Giovagnoli +1

In this paper, we prove that flat free boundaries of solutions to inhomogeneous one-phase Stefan problem are $C^{1, α}$ . The method consists of employing a hodograph transform and d…

Hölder gradient estimates for fractional p-caloric functions