Partial differential equations in economics Where, in economics, are partial differential equations used?

I'm particularly interested in micro theory applications, but would also be keen to know of other applications.
Here are a couple of suggestions. There are some PDEs in some recent continuous-time models, for instance in:


A Continuous-Time Version of the Principal-Agent Problem, by Sannikov, Review of Economic Studies (2008)
Persistent private information, by Williams, Econometrica (2011)


I would not be surprised if Yuliy Sannikov used PDEs in some of his other papers (although I have nothing precise in mind).

You can refer to the review by Achdou et al. (Partial differential equation models in macroeconomics, Philosophical Transactions of the Royal Society, 2014) for other references.