On the regularity of the polar factorization for time dependent maps

Details On the regularity of the polar factorization for time dependent maps On the regularity of the polar factorization for time dependent maps

2003-06-30

arxiv.org/abs/math/0306431v2

Mathematics

Analysis of PDEs

17 pages

Scientific paper

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.

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