The geometry of the space of Cauchy data of nonlinear PDEs

Giovanni Moreno

Open Mathematics (2013)

  • Volume: 11, Issue: 11, page 1960-1981
  • ISSN: 2391-5455

Abstract

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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.

How to cite

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Giovanni Moreno. "The geometry of the space of Cauchy data of nonlinear PDEs." Open Mathematics 11.11 (2013): 1960-1981. <http://eudml.org/doc/269260>.

@article{GiovanniMoreno2013,
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.},
author = {Giovanni Moreno},
journal = {Open Mathematics},
keywords = {Geometry of PDEs; Cauchy data; Lagrangian formalism; Fiber bundles; Jet spaces; Flags; flag bundles; geometry of partial differential equations; infinite-order bundles},
language = {eng},
number = {11},
pages = {1960-1981},
title = {The geometry of the space of Cauchy data of nonlinear PDEs},
url = {http://eudml.org/doc/269260},
volume = {11},
year = {2013},
}

TY - JOUR
AU - Giovanni Moreno
TI - The geometry of the space of Cauchy data of nonlinear PDEs
JO - Open Mathematics
PY - 2013
VL - 11
IS - 11
SP - 1960
EP - 1981
AB - 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.
LA - eng
KW - Geometry of PDEs; Cauchy data; Lagrangian formalism; Fiber bundles; Jet spaces; Flags; flag bundles; geometry of partial differential equations; infinite-order bundles
UR - http://eudml.org/doc/269260
ER -

References

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