11 papers
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…
Structure of the free interfaces near triple junction singularities in harmonic maps and optimal partition problems
Roberto Ognibene, Bozhidar Velichkov
We consider energy-minimizing harmonic maps into trees and we prove the regularity of the singular part of the free interface near triple junction points. Precisely, by proving a n…
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…
Fine structure of the two-phase Bernoulli free boundaries in 2D
Lorenzo Ferreri, Luca Spolaor, Bozhidar Velichkov
We prove that the branching set of a solution to a two-dimensional two-phase Bernoulli problem with constant coefficients is locally finite. We do this via a Weierstrass representa…
On the blow-up of the vectorial Bernoulli free boundary problem
Giovanni Siclari, Bozhidar Velichkov
In this paper, we complete the classification of the blow-up limits of minimizers of the vectorial Bernoulli free boundary problem. Furthermore, we study the vectorial Bernoulli fr…
Vectorial Bernoulli Problems and Free Boundary Systems
Giorgio Tortone, Bozhidar Velichkov
In this survey we go through some of the recent results about the regularity of vectorial free boundary problems of Bernoulli type and free boundary systems. The aim is to illustra…