Abstract:
We prove upper and lower bounds for the leading coefficient of Kolchin
dimension polynomial of systems of partial linear differential
equations in the case of codimension two, quadratic with respect to the orders of
the equations in the system. A notion of typical differential
dimension plays an important role in differential algebra, some
of its estimations were proved by J. Ritt and E. Kolchin; they also
advanced several conjectures that were later refuted. Our bound
generalizes the analogue of the Bézout theorem
for one differential indeterminate.
It is better than an estimation proved by D. Grigoriev.
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