We demonstrate under some assumptions on f(+), f(-) that a solution to the
classical Monge-Kantorovich problem of optimally rearranging the measure mu
(+) = f(+)dx onto mu(-) = f(-)dy call be constructed by studying the p-Lapl
acian equation
-div(/Du(p)/(p-2)Du(p)) = f(+) - f(-)
the limit as p --> infinity. The idea is to show u(p) --> u, where u satisf
ies
/Du/ less than or equal to 1, -div(aDu) = f(+) - f(-)
for some density a greater than or equal to 0, and then to build a Row by s
olving a nonautonomous ODE involving a, Du. f(+) and f(-).