Spencer δ-cohomology, restrictions, characteristics and involutive symbolic PDEs
Abstract
We generalize the notion of involutivity to systems of differential equations
of different orders and show that the classical results relating involutivity,
restrictions, characteristics and characteristicity, known for first
order systems, extend to the general context. This involves, in particular,
a new definition of strong characteristicity. The proof exploits a spectral
sequence relating Spencer δ-cohomology of a symbolic system and its
restriction to a non-characteristic subspace.
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