199 citations · 522 across the 42 of their papers we have counts for
5 papers · 1 filter
From volume cone to metric cone in the nonsmooth setting
Nicola Gigli, Guido de Philippis
We prove that `volume cone implies metric cone' in the setting of RCD spaces, thus generalising to this class of spaces a well known result of Cheeger-Colding valid in Ricci-limit…
A nonautonomous chain rule in and
Luigi Ambrosio, Graziano Crasta, Virginia De Cicco +1
In this paper we consider the chain rule formula for compositions in the case when has a Sobolev or BV regularity and is separately Sobolev, or B…
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…
BV Estimates in Optimal Transportation and Applications
Guido De Philippis, Alpár Mészáros, Filippo Santambrogio +1
In this paper we study the BV regularity for solutions of variational problems in Optimal Transportation. As an application we recover BV estimates for solutions of some non-linear…
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…