101 citations · 311 across the 55 of their papers we have counts for
70 papers
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…
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…
A rigidity result for a global vectorial free boundary problem with a linear datum
Giovanni Siclari, Bozhidar Velichkov
In this paper we completely classify the minimizers of a measure constraint global vectorial free boundary problem with a linear datum. More precisely, we show that there exists a…
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…
On a Multiphase Vectorial Bernoulli Free Boundary Problem
Giovanni Siclari, Bozhidar Velichkov
We study the regularity of minimizers of a multiphase vectorial Bernoulli free boundary problem. This problem consists in a minimization problem for the Bernoulli functional over f…