199 citations · 204 across the 8 of their papers we have counts for
6 papers · 1 filter
On singular strictly convex solutions to the Monge-Ampère equation
Guido De Philippis, Riccardo Tione
We show the existence of a strictly convex function with associated Monge-Ampère measure represented by a function with a.e. whose Hessian h…
From energy bounds to dimensional estimates in a branched transport model for type-I superconductors
Guido De Philippis, Michael Goldman, Berardo Ruffini
We consider a branched transport type problem which describes the magnetic flux through type-I superconductors in a regime of very weak applied fields. At the boundary of the sampl…
Rectifiability of varifolds with locally bounded first variation with respect to anisotropic surface energies
Guido De Philippis, Antonio De Rosa, Francesco Ghiraldin
We extend Allard's celebrated rectifiability theorem to the setting of varifolds with locally bounded first variation with respect to an anisotropic integrand. In particular, we id…
Existence of isoperimetric sets with densities "converging from below" in
Guido De Philippis, Giovanni Franzina, Aldo Pratelli
In this paper, we consider the isoperimetric problem in the space with density. Our result states that, if the density f is l.s.c. and converges to a positive limit…
Dimensional estimates for singular sets in geometric variational problems with free boundaries
Guido De Philippis, Francesco Maggi
We show that singular sets of free boundaries arising in codimension one anisotropic geometric variational problems are -negligible, where is the ambient spa…
A global existence result for the semigeostrophic equations in three dimensional convex domains
Luigi Ambrosio, Maria Colombo, Guido De Philippis +1
Exploiting recent regularity estimates for the Monge-Ampère equation, under some suitable assumptions on the initial data we prove global-in-time existence of Eulerian distribution…