7 papers
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\…
A strong quantitative form of the fractional isoperimetric inequality
Eleonora Cinti, Enzo Maria Merlino, Berardo Ruffini
We show a strong version of the fractional quantitative isoperimetric inequality, in which the isoperimetric deficit controls not only the Fraenkel asymmetry but also a sort of osc…
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…
Regularizing effects of absorption terms in local-nonlocal mild singular problems
Stefano Biagi, Enzo Maria Merlino, Eugenio Vecchi
In this paper we prove existence and uniqueness of energy solutionns for singular problems with absorption driven by local-nonlocal operators. Moreover, we establish a comparison p…
Barycentric stability of nonlocal perimeters: the convex case
Chiara Gambicchia, Enzo Maria Merlino, Berardo Ruffini +1
In this work, we establish a sharp form of a nonlocal quantitative isoperimetric inequality involving the barycentric asymmetry for convex sets. This result can be seen as the nonl…
Lipschitz regularity for almost minimizers of a one-phase -Bernoulli-type functional in Carnot Groups of step two
Fausto Ferrari, Enzo Maria Merlino
In this paper, in a Carnot group of step and homogeneous dimension , we prove that almost minimizers of the (horizontal) one-phase -Bernoulli-type functional…