4 papers · 2 filters
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…