35 citations · 38 across the 15 of their papers we have counts for
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A strong maximum principle for minimizers of the one-phase Bernoulli problem
Nick Edelen, Luca Spolaor, Bozhidar Velichkov
We prove a strong maximum principle for minimizers of the one-phase Alt-Caffarelli functional. We use this to construct a Hardt-Simon-type foliation associated to any 1-homogenous…
Free boundary cluster with Robin condition on the transmission Interface
Serena Guarino Lo Bianco, Domenico Angelo La Manna, Bozhidar Velichkov
We formulate and study a variational two-phase free boundary problem with Robin condition on the interface between the two phases, and we prove existence and regularity of solution…
(Quasi-)conformal methods in two-dimensional free boundary problems
Guido De Philippis, Luca Spolaor, Bozhidar Velichkov
In this paper we study the local behavior of solutions to some free boundary problems. We relate the theory of quasi-conformal maps to the regularity of the solutions to nonlinear…
Epsilon-regularity for the solutions of a free boundary system
Francesco Paolo Maiale, Giorgio Tortone, Bozhidar Velichkov
This paper is dedicated to a free boundary system arising in the study of a class of shape optimization problems. The problem involves three variables: two functions and , a…
Rectifiability and almost everywhere uniqueness of the blow-up for the vectorial Bernoulli free boundaries
Guido De Philippis, Max Engelstein, Luca Spolaor +1
We prove that for minimizers of the vectorial Alt-Caffarelli functional the two-phase singular set of the free boundary is rectifiable and the blow-up is unique almost everywhere o…
Regularity of the optimal sets for the second Dirichlet eigenvalue
Dario Mazzoleni, Baptiste Trey, Bozhidar Velichkov
This paper is dedicated to the regularity of the optimal sets for the second eigenvalue of the Dirichlet Laplacian. Precisely, we prove that if the set minimizes the functional…