English

On the regularity of the polar factorization for time dependent maps

Analysis of PDEs 2016-09-07 v2

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.

Cite

@article{arxiv.math/0306431,
  title  = {On the regularity of the polar factorization for time dependent maps},
  author = {G. Loeper},
  journal= {arXiv preprint arXiv:math/0306431},
  year   = {2016}
}

Comments

17 pages

R2 v1 2026-07-22T16:55:49.728Z