# The geometry of the space of Cauchy data of nonlinear PDEs

Open Mathematics (2013)

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

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topGiovanni 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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