12 papers
The singular set in the thin Stefan problem
Matteo Carducci, Roberto Colombo, Clara Torres-Latorre
We study the singular set of the free boundary for solutions of the thin Stefan problem in , which models the melting of a thin sheet of ice over…
A minimizing cone from Cartan polynomials in the Alt-Caffarelli problem
Matteo Carducci, Bozhidar Velichkov
In this paper we study a class of 1-homogeneous solutions of the one-phase problem coming from the Cartan isoparametric cubic polynomials, which exist only in dimensions $d=5,8,14,…
Uniqueness of one-phase cones with isolated singularity
Matteo Carducci, Bozhidar Velichkov
We prove uniqueness of the blow-up at every singular point of the one-phase free boundary problem for which one blow-up has an isolated singularity. The result applies to Lipschitz…
Uniqueness of the blow-up for some Alt-Phillips cones
Matteo Carducci, Giorgio Tortone
We establish uniqueness of blow-ups, with sharp quantitative convergence, for several classes of singular minimizing cones in the Alt-Phillips problem, in the range . As…
Quark hierarchies and CP violation from the Siegel modular group
M. Carducci, D. Meloni, M. Parriciatu +1
We investigate theories of flavour based on genus modular invariance and analyze how fermion mass hierarchies can be generated in this context, in the vicinity of invariant p…
Smoothness and stability in the Alt-Phillips problem
Matteo Carducci, Giorgio Tortone
We study the one-phase Alt-Phillips free boundary problem, focusing on the case of negative exponents . The goal of this paper is twofold. On the one hand, we prove sm…
Free boundary regularity for a tumor growth model with obstacle
Giulia Bevilacqua, Matteo Carducci
We develop an existence and regularity theory for solutions to a geometric free boundary problem motivated by models of tumor growth. In this setting, the tumor invades an accessib…
Existence and regularity in the fully nonlinear one-phase free boundary problem
Matteo Carducci, Bozhidar Velichkov
We consider viscosity solution to one-phase free boundary problems for general fully nonlinear operators and free boundary condition depending on the normal vector. We show existen…
Generic regularity of free boundaries in the obstacle problem for the fractional Laplacian
Matteo Carducci, Roberto Colombo
We establish generic regularity results of free boundaries for solutions of the obstacle problem for the fractional Laplacian . We prove that, for almost every obstacle, th…
An epiperimetric inequality for odd frequencies in the thin obstacle problem
Matteo Carducci, Bozhidar Velichkov
We prove for the first time an epiperimetric inequality for the thin obstacle Weiss' energy with odd frequencies and we apply it to solutions to the thin obstacle problem with gene…
Epiperimetric inequalities in the obstacle problem for the fractional Laplacian
Matteo Carducci
Using the epiperimetric inequalities approach, we study the obstacle problem for the fractional Laplacian with obstacle $φ\in C^{k,γ}(\mathbb{R}^n…
Optimal regularity of the thin obstacle problem by an epiperimetric inequality
Matteo Carducci
The key point to prove the optimal regularity of the thin obstacle problem is that the frequency at a point of the free boundary , say ,…