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Convex integration of non-linear systems of partial differential equations

David Spring — 1983

Annales de l'institut Fourier

Geometrical techniques are employed to prove a global existence theorem for C r -solutions to underdetermined systems of non-linear r t h order partial differential equations, r { 1 , 2 , 3 , ... } , which satisfy certain convexity conditions. The solutions are not unique, but satisfy given approximations on lower order derivatives. The main result, which includes the relative case generalizes the work of M. Gromov on non-linear first order systems.

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