35 citations · 82 across the 31 of their papers we have counts for
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Free boundary regularity for a multiphase shape optimization problem
Luca Spolaor, Baptiste Trey, Bozhidar Velichkov
In this paper we prove a regularity result in dimension two for almost-minimizers of the constrained one-phase Alt-Caffarelli and the two-phase Alt-Caffarelli-Friedman fu…
On the asymptotic behavior of the solutions to parabolic variational inequalities
Maria Colombo, Luca Spolaor, Bozhidar Velichkov
We consider various versions of the obstacle and thin-obstacle problems, we interpret them as variational inequalities, with non-smooth constraint, and prove that they satisfy a ne…
(Log-)epiperimetric inequality and regularity over smooth cones for almost Area-Minimizing currents
Max Engelstein, Luca Spolaor, Bozhidar Velichkov
We prove a new logarithmic epiperimetric inequality for multiplicity-one stationary cones with isolated singularity by flowing in the radial direction any given trace along appropr…
Uniqueness of the blow-up at isolated singularities for the Alt-Caffarelli functional
Max Engelstein, Luca Spolaor, Bozhidar Velichkov
In this paper we prove uniqueness of blow-ups and -regularity for the free-boundary of minimizers of the Alt-Caffarelli functional at points where one blow-up has an is…