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Constructing jet bundles from a cocycle of smooth transition functions

You start with the trivializations $S \times U_i \to U_i$ over your cover. Let me presume that you can take for granted the construction of the jet bundles $J^r(S \times U_i) \to U_i$, whose typical f …
Igor Khavkine's user avatar
4 votes

In which sense are Euler-Lagrange PDE's on fiber bundles quasi-linear?

Let $\mathcal{E} \subset J^{2k}E$ be the submanifold (provided that this subset is a submanifold) of all $2k$-jets sitting in the zero-level set of $\rho(E(\mathscr{L}))$, the PDE submanifold. …
Igor Khavkine's user avatar
4 votes
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A very basic question about projections in formal PDE theory

Your conjecture is almost correct. But consider the extreme case when your equation has no integrability conditions, so that $\operatorname{coker}(\sigma(\rho_{q+1} P)) = 0$, whence $\rho^{(1)}_{q+1}( …
Igor Khavkine's user avatar