10 papers
Hölder gradient estimates for fractional -caloric functions
Davide Giovagnoli, David Jesus, Luis Silvestre
We establish interior regularity estimates, for some , for fractional -caloric functions when is in the range . As a consequence, we deduc…
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…
Weighted Perimeters and pth Moments of Inertia of Convex Curves and Surfaces
Gyula Csató, Davide Giovagnoli, Prosenjit Roy
We study a shape optimization problem among convex bodies in that minimize or maximize weighted perimeters of the form $\int_{\partialΩ} ϕ(|x|) \, \mathrm{d} H^{n-1}…
A quantitative Hopf-Oleinik lemma for degenerate fully nonlinear operators and applications to free boundary problems
Davide Giovagnoli, Enzo Maria Merlino, Diego Moreira
We prove a quantitative inhomogeneous Hopf-Oleinik lemma for viscosity solutions of and, more generally, for viscosity supersolutions of $|\nabla u|^α\…
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…
regularity for fractional -harmonic functions
Davide Giovagnoli, David Jesus, Luis Silvestre
We establish interior regularity estimates for some , for solutions of the fractional -Laplace equation when is in the range $p \in [2,2/(1-…
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…
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…
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 . The method consists of employing a hodograph transform and d…
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…