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Dec 6, 2023 at 4:37 comment added Willie Wong Sorry, when transcribing I dropped the tildes, they should be $\tilde{F}$. // If $F$ is assumed to be injective, then the analysis in the first part is not needed. You just need to look at the final part about the factorization problem.
Dec 6, 2023 at 4:34 history edited Willie Wong CC BY-SA 4.0
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Dec 6, 2023 at 4:26 comment added Sardine Thanks for the thorough answer, I'll need some time to digest it! Could you clarify why you mention an assumption that $\partial F$ is symmetric? The reason I introduced a matrix $M$ such that $\partial F = gM$ is that $\partial F$ is not symmetric. This may be a minor detail. I also didn't think to mention that $F$ is assumed injective over a domain (smooth, convex) $E$.
Dec 6, 2023 at 3:41 history answered Willie Wong CC BY-SA 4.0