Nous utilisons une méthode probabiliste pour transformer le célèbre problème de Monge–Kantorovich dans une région bornée du plan Euclidien à celui de Dirichlet associé à une équation aux dérivées partielles quasi-linéaire :
We use a simple probability method to transform the celebrated Monge–Kantorovich problem in a bounded region of Euclidean plane into a Dirichlet boundary problem associated to a quasi-linear elliptic equation with 0-order term missing in its diffusion coefficients:
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@article{CRMATH_2010__348_5-6_267_0, author = {Shen, Yinfang and Zheng, Weian}, title = {On {Monge{\textendash}Kantorovich} problem in the plane}, journal = {Comptes Rendus. Math\'ematique}, pages = {267--271}, publisher = {Elsevier}, volume = {348}, number = {5-6}, year = {2010}, doi = {10.1016/j.crma.2009.11.022}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.crma.2009.11.022/} }
TY - JOUR AU - Shen, Yinfang AU - Zheng, Weian TI - On Monge–Kantorovich problem in the plane JO - Comptes Rendus. Mathématique PY - 2010 SP - 267 EP - 271 VL - 348 IS - 5-6 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2009.11.022/ DO - 10.1016/j.crma.2009.11.022 LA - en ID - CRMATH_2010__348_5-6_267_0 ER -
%0 Journal Article %A Shen, Yinfang %A Zheng, Weian %T On Monge–Kantorovich problem in the plane %J Comptes Rendus. Mathématique %D 2010 %P 267-271 %V 348 %N 5-6 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2009.11.022/ %R 10.1016/j.crma.2009.11.022 %G en %F CRMATH_2010__348_5-6_267_0
Shen, Yinfang; Zheng, Weian. On Monge–Kantorovich problem in the plane. Comptes Rendus. Mathématique, Tome 348 (2010) no. 5-6, pp. 267-271. doi : 10.1016/j.crma.2009.11.022. http://www.numdam.org/articles/10.1016/j.crma.2009.11.022/
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