Abstract
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.
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Moreno, G. The geometry of the space of Cauchy data of nonlinear PDEs. centr.eur.j.math. 11, 1960–1981 (2013). https://doi.org/10.2478/s11533-013-0292-y
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DOI: https://doi.org/10.2478/s11533-013-0292-y