On the regularity of the polar factorization for time dependent maps

2003/06/30 by Loeper, G. · 2 citations
#35j65 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.math/0306431

Abstract

We consider the polar factorization of vector valued mappings introduced by Y. Brenier. In the case of a family of mappings depending on a parameter. We investigate the regularity with respect to this parameter of the terms of the polar factorization by constructing some a priori bounds. To do so, we consider the linearization of the associated Monge-Ampere equation which we view as a conservation law.

Cited by

• A Generalization of Caffarelli's Contraction Theorem to Nearly Spherical Manifolds
• Local potential and Hölder estimates for the linearized Monge-Ampère equation

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