Manuscript submitted to doi:10.3934/xx.xx.xx.xx AIMS ’ Journals Volume X, Number 0X, XX 200X pp. X{XX OPTIMAL MATCHING PROBLEMS WITH COSTS GIVEN BY FINSLER DISTANCES

(Communicated by the associate editor name) Abstract. In this paper we deal with an optimal matching problem, that is, we want to transport two commodities (modeled by two measures that encode the spacial distribution of each commodity) to a given location, where they will match, minimizing the total transport cost that in our case is given by the sum of the two different Finsler distances that the two measures are transported. We perform a method to approximate the matching measure and the pair of Kantorovich potentials associated with this problem taking limit as p!1 in a variational system of pLaplacian type. 1. Introduction. I