Calculus of Variations and Geometric Measure Theory
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L. Caravenna

A proof of Sudakov theorem with strictly convex norms

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

[BibTeX]

Preprint

Inserted: 18 jan 2009
Last Updated: 19 jan 2009

Year: 2009
Notes:

Preprint SISSA 642008M


Abstract:

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.


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