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Weak regularity of Gauss mass transport.

Mon, 08/17/2009 - 18:30 — SomNambul
Authors: Alexander V. Kolesnikov
Subjects: Functional Analysis
link: http://arxiv.org/abs/0904.1852
Abstract

Given two probability measures $\mu$ and $\nu$ we consider a mass
transportation mapping $T$ satisfying 1) $T$ sends $\mu$ to $\nu$, 2) $T$ has
the form $T = \varphi \frac{\nabla \varphi}{|\nabla \varphi|}$, where $\varphi$
is a function with convex sublevel sets. We prove a change of variables formula
for $T$. We also establish some a priori estimates for $T$, and a new form of
the parabolic maximum principle. In addition, we discuss relations to the
Monge--Kantorovich problem, curvature flows theory, and parabolic nonlinear
PDE's.

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