3 papers
math.AP2025
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…
math.AP2024
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…
math.AP2023
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 ,…