Calculus of Variations and Geometric Measure Theory

A. Pratelli

On the sufficiency of $c$-cyclical monotonicity for optimality of transport plans

created by pratelli on 20 Nov 2006
modified on 25 Sep 2010


Published Paper

Inserted: 20 nov 2006
Last Updated: 25 sep 2010

Journal: Math. Z.
Year: 2007


We consider a mass transport problem among Polish spaces, and we show that a transport plan concentrated in a $c-$cyclical monotone set is optimal if the cost function is continuous and possibly $+\infty$ valued; the same result is proved for a generic l.s.c. cost function in the case when the measures are purely atomic. This generalizes the previously known results.