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Elliptic, parabolic and hyperbolic operators. Laplace, Laplace-Beltrami, Schrödinger, Dirac. Exterior derivative and Lie derivative operators.

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Finding thin plate spline subjected to boundary conditions

I am trying to formulate a problem as a PDE. What I want to know is if my formulation is correct, if it admits solution and what am I missing. This question is related to : Thin-Plate-Spline understan …
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