Sorry for the terribly vague title; I just can't think of a better name for the thread.(adsbygoogle = window.adsbygoogle || []).push({});

I'm interested in functions ##f:[0,1]^2\to\mathbb{R}## which solve the DE, ##\tfrac{\partial}{\partial y} f(y, x) = -\tfrac{\partial}{\partial x} f(x,y) ##.

I know this is a huge collection of functions, amounting to everything of the form ##\left\{ \int g(x,y) dx: \ g \text{ antisymmetric} \right\}##, but I'm wondering whether there's a nice description of the family of functions ##f## satisfying the equation. Ideally, I'd like a description which doesn't use derivatives or integrals.

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# A Functions with "antisymmetric partial"

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