5 papers · 1 filter
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…
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…