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Area and coarea formulas for the mappings of Sobolev classes with values in a metric space

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Abstract

We prove the metric differentiability and approximate metric differentiability for some broad classes of mappings with values in a metric space, including Sobolev classes. By way of application, we derive some metric analogs of area and coarea formulas.

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Authors and Affiliations

  1. Novosibirsk State University, Novosibirsk, Russia

    M. B. Karmanova

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  1. M. B. Karmanova
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__________

Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 48, No. 4, pp. 778–788, July–August, 2007.

Original Russian Text Copyright © 2007 Karmanova M. B.

The author was partially supported by the Russian Foundation for Basic Research (Grant 05-01-00482) and the State Maintenance Program for the Junior Scientists and the Leading Scientific Schools of the Russian Federation (Grant NSh-8526.2006.1).

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Karmanova, M.B. Area and coarea formulas for the mappings of Sobolev classes with values in a metric space. Sib Math J 48, 621–628 (2007). https://doi.org/10.1007/s11202-007-0064-7

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  • DOI: https://doi.org/10.1007/s11202-007-0064-7

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