3 papers
math.AP2026
Energy dissipation and free boundary stability of the Stefan problem
Filippo Paiano, Bozhidar Velichkov
In this paper we prove the stability and the continuity of the free boundaries of two-phase and one-phase weak solutions to the Stefan problem in any dimension. Our proof has two m…
math.AP2026
An elliptic regularization approach to the Stefan problem
Filippo Paiano, Bozhidar Velichkov
In this paper, we develop the theory for the two-phase Stefan problem with finite energy, possibly non-empty mushy region, and space-dependent melting temperature. Specifically, we…
math.AP2025
Regularity for free boundary surfaces minimizing degenerate area functionals
Carlo Gasparetto, Filippo Paiano, Bozhidar Velichkov
We establish an epsilon-regularity theorem at points in the free boundary of almost-minimizers of the energy $\mathrm{Per}_{w}(E)=\int_{\partial^*E}w\,\mathrm{d} {\mathscr{H}}^{n-1…