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.
@article{bwmeta1.element.doi-10_2478_s11533-013-0292-y,
author = {Giovanni Moreno},
title = {The geometry of the space of Cauchy data of nonlinear PDEs},
journal = {Open Mathematics},
volume = {11},
year = {2013},
pages = {1960-1981},
zbl = {1292.35011},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-013-0292-y}
}
Giovanni Moreno. The geometry of the space of Cauchy data of nonlinear PDEs. Open Mathematics, Tome 11 (2013) pp. 1960-1981. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-013-0292-y/
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