Central European Journal of Mathematics

, Volume 11, Issue 11, pp 1960–1981 | Cite as

The geometry of the space of Cauchy data of nonlinear PDEs

  • Giovanni MorenoEmail author
Research Article


First-order jet bundles can be put at the foundations of the modern geometric approach to nonlinear PDEs, since higher-order jet bundles can be seen as constrained iterated jet bundles. The definition of first-order jet bundles can be given in many equivalent ways — for instance, by means of Grassmann bundles. In this paper we generalize it by means of flag bundles, and develop the corresponding theory for higher-oder and infinite-order jet bundles. We show that this is a natural geometric framework for the space of Cauchy data for nonlinear PDEs. As an example, we derive a general notion of transversality conditions in the Calculus of Variations.


Geometry of PDEs Cauchy data Lagrangian formalism Fiber bundles Jet spaces Flags 


14M15 35A99 53B15 53C80 57R99 58A20 


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© Versita Warsaw and Springer-Verlag Wien 2013

Authors and Affiliations

  1. 1.Mathematical Institute in OpavaSilesian University in OpavaOpavaCzech Republic

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