Geodesic
Universal prolongation of linear partial differential equations on filtered manifolds
Archivum mathematicum, Tome 45 (2009) no. 4, pp. 289-300.

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The aim of this article is to show that systems of linear partial differential equations on filtered manifolds, which are of weighted finite type, can be canonically rewritten as first order systems of a certain type. This leads immediately to obstructions to the existence of solutions. Moreover, we will deduce that the solution space of such equations is always finite dimensional.
Classification : 35N05, 53D10, 58A20, 58A30, 58H10, 58J60
Keywords: prolongation; partial differential equations; filtered manifolds; contact manifolds; weighted jet bundles 
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     author = {Neusser, Katharina},
     title = {Universal prolongation of linear partial differential equations on filtered manifolds},
     journal = {Archivum mathematicum},
     pages = {289--300},
     publisher = {mathdoc},
     volume = {45},
     number = {4},
     year = {2009},
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     zbl = {1212.35332},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_2009__45_4_a5/}
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Neusser, Katharina. Universal prolongation of linear partial differential equations on filtered manifolds. Archivum mathematicum, Tome 45 (2009) no. 4, pp. 289-300. http://geodesic.mathdoc.fr/item/ARM_2009__45_4_a5/