Calculus of Variations and Geometric Measure Theory

L. Caravenna

A proof of Sudakov theorem with strictly convex norms

created by caravenna on 18 Jan 2009
modified on 19 Jan 2009



Inserted: 18 jan 2009
Last Updated: 19 jan 2009

Year: 2009

Preprint SISSA 642008M


We establish a solution to the Monge problem in ${R}^{N}$, with an asymmetric, {strictly convex} norm cost function, when the initial measure is absolutely continuous. We focus on the strategy, based on disintegration of measures, initially proposed by Sudakov. As known, there is a gap to fill. The missing step is completed when the unit ball is strictly convex, but not necessarily differentiable nor uniformly convex. The key disintegration is achieved following a similar proof for a variational problem.