35 citations · 45 across the 13 of their papers we have counts for
15 papers · 1 filter
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…
Structure of two-dimensional mod area-minimizing currents near flat singularities: the codimension one case
Anna Skorobogatova, Luca Spolaor, Salvatore Stuvard
We obtain a fine structural result for two-dimensional mod area-minimizing currents of codimension one, close to flat singularities. Precisely, we show that, locally around an…
Rectifiability of the singular set and uniqueness of tangent cones for semicalibrated currents
Paul Minter, Davide Parise, Anna Skorobogatova +1
We prove that the singular set of an -dimensional integral current in , semicalibrated by a -form is countably -rectifiable.…
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…
Fine structure of the singular set of area minimizing hypersurfaces modulo
Camillo De Lellis, Jonas Hirsch, Andrea Marchese +2
Consider an area minimizing current modulo of dimension in a smooth Riemannian manifold of dimension . We prove that its interior singular set is, up to a relatively c…
(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…