I am aware of Hurwickz Uzawa work in integability, neatly summarized by Border http://people.hss.caltech.edu/~kcb/Notes/Demand4-Integrability.pdf I am wondering if there is any modern treatment of the subject, for instance a version in Sobolev spaces, or taking advantage of new tools in PDE from Lie Algebra. In particular, I am interested in work that extends the integrability problem to non-linear budget constraints.
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2You could take a look at Ivar Ekeland's work on using exterior differential calculus to deal with aggregation problems. – Michael Greinecker May 22 '15 at 19:39