On the regularity of the polar factorization for time dependent maps

G. Loeper

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On the regularity of the polar factorization for time dependent maps

G. Loeper

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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.

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G. Loeper. 2005-04-07. On the regularity of the polar factorization for time dependent maps. https://arxiv.org/abs/math/0306431

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