We study some problems of optimal distribution masses, and we show that they can be characterized by a suitable Monge-Kantorovich equation. In the case scalar state functions, equivalence with mass transport problem, emphasizing its geometrical approach through geodesics. The elasticity, where function is vector valued, also considered. both cases examples are presented.

Abstract Rigorous results concerning the possibility of homogenizing a set parallel fibres are given from viewpoint electromagnetic scattering. We deal with classical time-harmonic Maxwell problem and distinguish two cases polarization, i.e. electric field to (E∥) magnetic (H∥). Assuming low density fibres, we obtain, in E∥ case, an effective medium possibly negative permittivity, whereas H∥ case disappear completely. On other hand, for high leads perfectly conducting dielectric surface...

We study a class of optimal transport planning problems where the reference cost involves non-linear function G ( x, p ) representing between Dirac measure δ x and target probability . This allows to consider interesting models which favour multi-valued maps in contrast with classical linear case $G(x,p)=\int c(x,y)dp$ finding single-valued is key issue. present an existence result general duality principle apply many examples. Moreover, under suitable subadditivity condition, we derive...

We study the problem of Michell trusses when system applied equilibrated forces is a vector measure with compact support. introduce class stress tensors which can be written as superposition rank-one carried by curves (lines principal strains). Optimality conditions are given for such families showing in particular that optimal mutually orthogonal curves. The method illustrated on specific example where uniqueness proved studying an unusual hyperbolic PDEs. questions we address here interest...

Abstract Our aim is to evidence new 3D composite diffractive structures whose effective permittivity tensor can exhibit very large positive or negative real eigenvalues. We use a reiterated homogenization procedure in which the first step consists considering bounded obstacle made of periodically disposed parallel high conducting metallic fibers finite length and thin cross section. As shown [2], resulting constitutive law non-local. Then by reproducing same kind at small scale, we obtain...

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 $f$.

une infraction pénale.Toute copie ou impression de ce fichier doit contenir la présente mention copyright.