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Sobolev Spaces in Mathematics II pp 311–327Cite as

Estimates for Completely Integrable Systems of Differential Operators and Applications

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Part of the book series: International Mathematical Series ((IMAT,volume 9))

Abstract

A criterion for the complete integrability of some class of systems of differential equations is established. In the proof, the corresponding system for a matrix-valued function Z of class W 1,p(Ω) is used. Applications to differential geometry (in particular, the stability in the Bonnet theorem) are discussed.

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References

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Authors and Affiliations

  1. Sobolev Institute of Mathematics SB RAS, 4 Pr. Koptyga, 630090 Novosibirsk, Russia

    Yuri Reshetnyak

Authors
  1. Yuri Reshetnyak
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Correspondence to Yuri Reshetnyak .

Editor information

Editors and Affiliations

  1. Department of Mathematics, Ohio State University, Columbus, USA

    Vladimir Maz'ya

  2. Department of Mathematical Sciences, University of Liverpool, Liverpool, UK

    Vladimir Maz'ya

  3. Department of Mathematics, Linköping University, Linköping, Sweden

    Vladimir Maz'ya

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Reshetnyak, Y. (2009). Estimates for Completely Integrable Systems of Differential Operators and Applications. In: Maz'ya, V. (eds) Sobolev Spaces in Mathematics II. International Mathematical Series, vol 9. Springer, New York, NY. https://doi.org/10.1007/978-0-387-85650-6_13

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