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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Yinfang Shen 1, 2 ; Weian Zheng 1, 2
@article{CRMATH_2010__348_5-6_267_0, author = {Yinfang Shen and Weian Zheng}, 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}, }
Yinfang Shen; Weian Zheng. On Monge–Kantorovich problem in the plane. Comptes Rendus. Mathématique, Volume 348 (2010) no. 5-6, pp. 267-271. doi : 10.1016/j.crma.2009.11.022. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2009.11.022/
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