<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">LUIGI DE PASCALE</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">THE MONGE PROBLEM IN R d : VARIATIONS ON A THEME II</style></title><secondary-title><style face="normal" font="default" size="100%">Communications in Applied Analysis</style></secondary-title><short-title><style face="normal" font="default" size="100%">MONGE’S PROBLEM</style></short-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">49J4</style></keyword><keyword><style  face="normal" font="default" size="100%">49K30</style></keyword><keyword><style  face="normal" font="default" size="100%">49Q20</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2011</style></year><pub-dates><date><style  face="normal" font="default" size="100%">08/2011</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://www.acadsol.eu/en/articles/15/3/5.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">15</style></volume><pages><style face="normal" font="default" size="100%">340</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;div class=&quot;rtejustify&quot;&gt;In some recent papers [11, 12] it is proved that, under natural assumptions on the first marginal, the Monge problem in the metric space R&lt;sup&gt;d&lt;/sup&gt; equipped with a general norm admits a solution. Although the basic idea of the solution is simple the proof involves some very complex technical results. Here we will report a proof of the result in the simpler case of uniformly convex norms. Uniform convexity allow us to reduce the technical burdens while still giving the main ideas of the general proof. The proof of the density of the transport set given in this paper is original.&lt;/div&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">3</style></issue><work-type><style face="normal" font="default" size="100%">scientific: mathematics</style></work-type><section><style face="normal" font="default" size="100%">325</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">THIERRY CHAMPION</style></author><author><style face="normal" font="default" size="100%">LUIGI DE PASCALE</style></author><author><style face="normal" font="default" size="100%">CHLOE JIMENEZ</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">THE ∞-EIGENVALUE PROBLEM AND A PROBLEM OF OPTIMAL TRANSPORTATION</style></title></titles><keywords><keyword><style  face="normal" font="default" size="100%">99Z00</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2009</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2009</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://www.acadsol.eu/en/articles/13/4/7.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">13</style></volume><pages><style face="normal" font="default" size="100%">19</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;The so-called eigenvalues and eigenfunctions of the infinite Laplacian ∆∞ are defined through an asymptotic study of that of the usual p-Laplacian ∆p, this brings to a characterization via a non-linear eigenvalue problem for a PDE satisfied in the viscosity sense. In this paper, we obtain an other characterization of the first eigenvalue via a problem of optimal transportation, and recover properties of the first eigenvalue and corresponding positive eigenfunctions.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">4</style></issue><section><style face="normal" font="default" size="100%">547</style></section></record></records></xml>