2003/08/21 by Ivar Ekeland, Ekeland, Ivar · 2 citations
Mathematics · #05C38 #15A15 #15A18 #Analysis of PDEs (math.AP) #FOS: Mathematics #Optimization and Control (math.OC) #Secondary 05A15 #math.AP #math.OC #msc:05A15 #msc:05C38 #msc:15A15 #msc:15A18
paper · pdf · doi:10.48550/arxiv.math/0308206
arxiv created 2003/08/21 · arxiv updated 2009/12/01
Given two measured spaces (X,dx), (Y,dy) and a third space Z, given two functions u(x,z) and v(x,z), we study the problem of finding two maps s from X to Z and t from Y to Z such that the images s(dx) and t(dy) coincide, and the integral of u(x,s(x))dx+v(y,t(y))dy is maximal. We give condition on u and v for which there is a unique solution.