Estimates for Completely Integrable Systems of Differential Operators and Applications

  • Yuri Reshetnyak
Part of the International Mathematical Series book series (IMAT, volume 9)


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.


Quadratic Form Fundamental Form Sobolev Embedding Theorem Bonnet Theorem Cauchy Condition 
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© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Sobolev Institute of Mathematics SB RASRussia

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