24 citations · 31 across the 4 of their papers we have counts for
9 papers
Optimal Besov differentiability for entropy solutions of the Eikonal equation
Francesco Ghiraldin, Xavier Lamy
In this paper we study the Eikonal equation in a bounded planar domain. We prove the equivalence among optimal Besov regularity, the finiteness of every entropy production and the…
Existence results for minimizers of parametric elliptic functionals
Guido De Philippis, Antonio De Rosa, Francesco Ghiraldin
We prove a compactness principle for the anisotropic formulation of the Plateau problem in any codimension, in the same spirit of the previous works of the authors \cite{DelGhiMag,…
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…
A direct approach to the anisotropic Plateau problem
Camillo De Lellis, Antonio De Rosa, Francesco Ghiraldin
We prove a compactness principle for the anisotropic formulation of the Plateau problem in codimension one, along the same lines of previous works of the authors [DGM14, DPDRG15].…
On the number of singular points for planar multivalued harmonic functions
Francesco Ghiraldin, Luca Spolaor
In this note we give a quantitative estimate on the number of singular points of multiplicity of a -dimensional -valued energy minimizing map, in terms of the value of it…
Structure of solutions of multidimensional conservation laws with discontinuous flux and applications to uniqueness
Graziano Crasta, Virginia De Cicco, Guido De Philippis +1
We investigate the structure of solutions of conservation laws with discontinuous flux under quite general assumption on the flux. We show that any entropy solution admits traces o…
A direct approach to Plateau's problem in any codimension
Guido De Philippis, Antonio De Rosa, Francesco Ghiraldin
This paper aims to propose a direct approach to solve the Plateau's problem in codimension higher than one. The problem is formulated as the minimization of the Hausdorff measure a…
A direct approach to Plateau's problem
Camillo De Lellis, Francesco Ghiraldin, Francesco Maggi
We provide a compactness principle which is applicable to different formulations of Plateau's problem in codimension one and which is exclusively based on the theory of Radon measu…
Compactness of special functions of bounded higher variation
Luigi Ambrosio, Francesco Ghiraldin
Given an open set Ω\subset\R^m and n>1, we introduce the new spaces GB_nV(Ω) of Generalized functions of bounded higher variation and GSB_nV(Ω) of Generalized special functions of…