TITLE

# A new class of transport distances between measures

AUTHOR(S)
Dolbeault, Jean; Nazaret, Bruno; Savar�, Giuseppe
PUB. DATE
February 2009
SOURCE
Calculus of Variations & Partial Differential Equations;Feb2009, Vol. 34 Issue 2, p193
SOURCE TYPE
DOC. TYPE
Article
ABSTRACT
We introduce a new class of distances between nonnegative Radon measures in $${\mathbb{R}^d}$$ . They are modeled on the dynamical characterization of the Kantorovich-Rubinstein-Wasserstein distances proposed by Benamou and Brenier (Numer Math 84:375ï¿½393, 2000) and provide a wide family interpolating between the Wasserstein and the homogeneous $${W^{-1,p}_\gamma}$$ -Sobolev distances. From the point of view of optimal transport theory, these distances minimize a dynamical cost to move a given initial distribution of mass to a final configuration. An important difference with the classical setting in mass transport theory is that the cost not only depends on the velocity of the moving particles but also on the densities of the intermediate configurations with respect to a given reference measure ?. We study the topological and geometric properties of these new distances, comparing them with the notion of weak convergence of measures and the well established Kantorovich-Rubinstein-Wasserstein theory. An example of possible applications to the geometric theory of gradient flows is also given.
ACCESSION #
34851611

## Related Articles

• Further confirmations of mass transfer in Algol type binary U Sagittae. Manzoori, Davood // Astrophysics & Space Science;Feb2008, Vol. 313 Issue 4, p339

This paper describes how a new photometric V light curve solution of Algol type binary U Sge was obtained using Wilsonâ€“Devinney code. I also discuss how the physical and orbital parameters, along with absolute dimensions of the system, were determined. The Roche lobe configurations of the...

• Rate of Convergence to Equilibrium for the Spatially Homogeneous Boltzmann Equation with Hard Potentials. Mouhot, Cl�ment // Communications in Mathematical Physics;Jan2006, Vol. 261 Issue 3, p629

For the spatially homogeneous Boltzmann equation with hard potentials and Grad's cutoff (e.g. hard spheres), we give quantitative estimates of exponential convergence to equilibrium, and we show that the rate of exponential decay is governed by the spectral gap for the linearized equation, on...

• S-CONVERGENCE. Nguetseng, Gabriel; Svanstedt, Nils // Banach Journal of Mathematical Analysis;2011, Vol. 5 Issue 1, p101

We discuss two new concepts of convergence in Lp-spaces, the socalled weak S-convergence and strong S-convergence, which are intermediate between classical weak convergence and strong convergence. We also introduce the concept of S-convergence for Radon measures. Our basic tool is the classical...

• Oxygen mass transfer in a 16.6 cm i. d. multiphase reciprocating plate column. Vasic1, Ljubi�a S.; Bankovic-Ilic, Ivana B.; Lazic, Miodrag L.; Veljkovic, Vlada B.; Skala, Dejan U. // Journal of the Serbian Chemical Society;May2007, Vol. 72 Issue 5, p523

The effects of vibration intensity, superficial gas velocity and content of solid particles on the volumetric oxygen mass transfer coefficient (k1a) in a 16.6 cm i.d. multiphase reciprocating plate column were strudied. The k1a increased with increasing vibration intensity and superficial gas...

• Effect of high mass fluxes on heat and mass transfer through a flat surface. Kar, S.; Chen, X. D. // Proceedings of the Institution of Mechanical Engineers -- Part E;2004, Vol. 218 Issue 4, p213

In the present case study, a highly idealized situation of an incompressible fluid flowing horizontally over a flat surface, consisting of a volatile liquid in a saturated state undergoing vaporization, is considered. The problem is similar to that reported by Bird et al. [1], but allowance is...

• Optimal Planar Flow Network Designs for Tissue Engineered Constructs with Built-in Vasculature. Vijayakumar Janakiraman; Kamlesh Mathur; Harihara Baskaran // Annals of Biomedical Engineering;Mar2007, Vol. 35 Issue 3, p337

Abstract??Convective delivery of nutrients is important to enhance mass transport within tissue engineered (TE) products. Depending on the target tissue, an ideal TE product will have an integrated microvasculature that will eliminate mass transport limitations that can occur during product...

• Oxidation kinetics of chromium in fine-particle TiO2-Cr2O3 Oxides. Belaya, E. A.; Viktorov, V. V. // Inorganic Materials;Jul2008, Vol. 44 Issue 7, p733

The mass transport during the oxidation of Cr2O3 in mixtures of fine-particle TiO2 and Cr2O3 in air has been studied at temperatures from 800 to 1000ï¿½C by magnetochemical analysis. The results indicate that the process leads to the oxidation of up to ten surface atomic layers. The mass...

• Interior regularity of optimal transport paths. Qinglan Xia // Calculus of Variations & Partial Differential Equations;Jul2004, Vol. 20 Issue 3, p283

In a previous paper, we considered problems for which the cost of transporting one probability measure to another is given by a transport path rather than a transport map. In this model overlapping transport is frequently more economical. In the present article we study the interior regularity...

• Effect of a Gasâ€Phase Reaction on the Combustion Performance of a Sandwich Layered System. Strunin, V. A.; Manelis, G. B. // Combustion, Explosion, & Shock Waves;May/Jun2004, Vol. 40 Issue 3, p270

This paper considers a sandwich layered combustion model (an oxidizer and a fuel) that takes into account condensed- and gas-phase chemical reactions and transverse heat and mass transfer. Under particular simplifications, algebraic expressions are obtained for the burning rates of the...

Share