The geometry of the space of Cauchy data of nonlinear PDEs

Giovanni Moreno 1
  • 1 Mathematical Institute in Opava, Silesian University in Opava, Na Rybničku 626/1, 746 01, Opava, Czech Republic

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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