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On the regularity of the polar factorization for time dependent maps

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Abstract.

We consider the polar factorization of vector valued mappings, introduced in [3], 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-Ampére equation.

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Authors and Affiliations

  1. Département de Mathématiques, Université de Nice Sophia-Antipolis, Parc Valrose, 06108, Nice Cedex 2, France

    G. Loeper

  2. Departement of Mathematics, Fields Institute, 222 College Street, M5T 3Y1, Toronto, Ontario, Canada

    G. Loeper

  3. Department of Mathematics, University of Toronto, M5G 3C3, Toronto, Ontario, Canada

    G. Loeper

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  1. G. Loeper
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Correspondence to G. Loeper.

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Received: 28 July 2003, Accepted: 5 April 2004, Published online: 16 July 2004

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Loeper, G. On the regularity of the polar factorization for time dependent maps. Calc. Var. 22, 343–374 (2005). https://doi.org/10.1007/s00526-004-0280-y

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  • DOI: https://doi.org/10.1007/s00526-004-0280-y

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