Timeline for Does "solutions of an $n$-th order ODE form an $n$-dimensional vector space" somehow generalise to PDEs?
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| Oct 2, 2015 at 12:46 | comment | added | Jeanne Clelland | Yes, as long as the coefficients of the PDE are real analytic; this follows from the Cartan-Kahler theorem in exterior differential systems. | |
| Oct 2, 2015 at 5:55 | comment | added | Qiaochu Yuan | Right, it's clear what the intuition is, but can this actually be made rigorous the same way that dimensions of vector spaces can be made rigorous? For example, is it clear that the "counts" you obtain in this way are necessarily unique? | |
| Oct 2, 2015 at 3:04 | history | answered | Jeanne Clelland | CC BY-SA 3.0 |