In the classical Monge–Kantorovich problem, transportation cost depends only on amount of mass sent from sources to destinations and not paths followed by this mass. Thus, it does allow for congestion effects. Using notion traffic intensity, we propose a variant, taking into account congestion. This variant is continuous version well-known problem networks that studied both in economics operational research. The interest its relations with equilibria Wardrop type. What prove paper exactly...

Starting from the work by Brenier [Extended Monge–Kantorovich theory, in Optimal Transportation and Applications (Martina Franca 2001), Lecture Notes Math. 1813, Springer-Verlag, Berlin (2003), pp. 91–121], where a dynamic formulation of mass transportation problems was given, we consider more general framework, different kinds cost functions are allowed. This seems relevant some presenting congestion effects as, for instance, traffic on highway, crowds moving domains with obstacles, and,...

Consider a distribution of citizens in an urban area which some services (supermarkets, post offices. . ) are present. Each citizen, order to use service, spends amount time is due both the travel service and queue waiting service. The choice be used made by every citizen served more quickly. Two types problems can considered: global optimization total spent whole city (we define optimum we study it with techniques from optimal mass transportation) individual optimization, each chooses...

We investigate a two players zero sum differential game with incomplete information on the initial state: The first player has private state while second knows only probability distribution state. This could be view as generalization to games of famous Aumann-Maschler framework for repeated games. In an article author, existence value in random strategies was obtained finite number conditions (the is combination Dirac measures). main novelty present work consists : extending result infinite...

Let $\Omega$ be a bounded Lipschitz regular open subset of $\mathbb {R}^d$ and let $\mu ,\nu$ two probablity measures on $\overline {\Omega }$. It is well known that if =f dx$ absolutely continuous, then there exists, for every $p>1$, unique transport map $T_p$ pushing forward $\mu$ $\nu$ which realizes the Monge-Kantorovich distance $W_p(\mu ,\nu )$. In this paper, we establish an $L^\infty$ bound displacement $T_p x-x$ depends only $p$, shape essential infimum density $f$.

The so-called eigenvalues and eigenfunctions of the infinite Laplacian $Δ_\infty$ are defined through an asymptotic study that usual $p$-Laplacian $Δ_p$, this brings to a characterization via non-linear eigenvalue problem for PDE satisfied in viscosity sense. In paper, we obtain other first optimal transportation, recover properties corresponding positive eigenfunctions.

We prove existence and uniqueness of solutions for a system PDEs which describes the growth sandpile in silos with flat bottom under action vertical, measure source. The tools we use are discrete approximation source duality theory optimal transport (or Monge-Kantorovich) problems.

<p style='text-indent:20px;'>We study a two player zero sum game where the initial position <inline-formula><tex-math id="M1">\begin{document}$ z_0 $\end{document}</tex-math></inline-formula> is not communicated to any player. The function of couple id="M2">\begin{document}$ (x_0,y_0) id="M3">\begin{document}$ x_0 Ⅰ while id="M4">\begin{document}$ y_0 Ⅱ. id="M5">\begin{document}$ chosen according probability measure id="M6">\begin{document}$ dm(x,y) = h(x,y) d\mu(x) d\nu(y)...

We prove existence and uniqueness of solutions for a system PDEs which describes the growth sandpile in silos with flat bottom under action vertical, measure source. The tools we use are discrete approximation source duality theory optimal transport (or Monge-Kantorovich) problems.

We prove existence of an optimal transport map in the Monge-Kantorovich problem associated to a cost $c(x,y)$ which is not finite everywhere, but coincides with $|x-y|^2$ if displacement $y-x$ belongs given convex set $C$ and it $+\infty$ otherwise. The result proven for satisfying some technical assumptions allowing any body $\R^2$ polyhedron $\R^d$, $d>2$. tools are inspired by recent Champion-DePascale-Juutinen technique. Their idea, based on density points avoiding disintegrations dual...

Several optimal control problems in , like systems with uncertainty, of flock dynamics, or multiagent systems, can be naturally formulated the space probability measures . This leads to study dynamics and viscosity solutions Hamilton–Jacobi–Bellman equation satisfied by value functions those problems, both stated Wasserstein measures. Since this also viewed as set laws random variables a suitable space, main aim paper is such investigate relations between dynamical their representations from...

Consider a distribution of citizens in an urban area which some services (supermarkets, post offices...) are present. Each citizen, order to use service, spends amount time is due both the travel service and queue waiting service. The choice be used made by every citizen served more quickly. Two types problems can considered: global optimization total spent whole city (we define optimum we study it with techniques from optimal mass transportation) individual optimization, each chooses trying...