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A simple model to handle the flow of people in emergency evacuation situations is considered: at every point x, the velocity U(x) that individuals at x would like to realize is given. Yet, the… (More)

- Guillaume Carlier, Carlos Jimenez, Filippo Santambrogio
- SIAM J. Control and Optimization
- 2006

In the classical Monge-Kantorovich problem, the transportation cost only depends on the amount of mass sent from sources to destinations and not on the paths followed by this mass. Thus, it does not… (More)

The paper presents some short proofs for transport density absolute continuity and Lp estimates. Most of the previously existing results which were proven by geometric arguments are re-proved through… (More)

- Guillaume Carlier, Alfred Galichon, Filippo Santambrogio
- SIAM J. Math. Analysis
- 2008

A simple procedure to map two probability measures in $\mathbb{R}^d$ is the so-called \emph{Knothe-Rosenblatt rearrangement}, which consists in rearranging monotonically the marginal distributions of… (More)

Abstract Starting from a model of traffic congestion, we introduce a minimal-flow-like variational problem whose solution is characterized by a very degenerate elliptic PDE. We precisely investigate… (More)

We consider the problem of the optimal location of a Dirichlet region in a two-dimensional domain $\Omega$ subject to a force $f$ in order to minimize the compliance of the configuration. The class… (More)

Given a metric space $X$ we consider a general class of functionals which measure the cost of a path in $X$ joining two given points $x_0$ and $x_1$, providing abstract existence results for optimal… (More)

The Mα energy which is usually minimized in branched transport problems among singular one-dimensional rectifiable vector measures is approximated by means of a sequence of elliptic energies defined… (More)

Given the probability measure ν over the given region Ω ⊂ R n , we consider the op- timal location of a set Σ composed by n points in Ω in order to minimize the average distance Σ � � Ω dist (x, Σ)… (More)