Timeline for Are linearizations of involutive PDEs locally solvable?
Current License: CC BY-SA 3.0
8 events
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| Mar 24, 2015 at 20:42 | comment | added | Orn Arnaldsson | Many thanks for taking the time to work through this. Maybe I can now convince Peter and his collaborator on the pseudogroup paper to drop the extra condition. | |
| Mar 24, 2015 at 1:21 | comment | added | Deane Yang | The step in the Cartan-Kahler theorem that I didn't find obvious is the dimension of the space of formal 2nd order solutions to the linearized system. The last paragraph of my answer shows how to get this from the involutivity of the nonlinear system. | |
| Mar 23, 2015 at 23:14 | comment | added | Deane Yang | The inhomogeneous case requires only that the inhomogeneous term satisfy compatibility conditions, which are equivalent to saying that the system has at least one formal 2nd order solution. | |
| Mar 23, 2015 at 20:26 | comment | added | Orn Arnaldsson | I agree that this is pretty easy in the homogeneous case, and when I work through the proof of Cartan-Kahler I can't see where the local solvability for the linearized system fails, but I wanted to double check on MO. | |
| Mar 23, 2015 at 20:22 | comment | added | Deane Yang | Unfortunately, by now I find my own monograph unreadable. | |
| Mar 23, 2015 at 20:20 | history | edited | Deane Yang | CC BY-SA 3.0 |
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| Mar 23, 2015 at 19:20 | history | edited | Deane Yang | CC BY-SA 3.0 |
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| Mar 23, 2015 at 17:58 | history | answered | Deane Yang | CC BY-SA 3.0 |