I came across this differential equation. I'm not sure if it's research level, but I think it might be:

$$u\frac{\partial}{\partial u}\left(u\frac{\partial f}{\partial u}\right) + v\frac{\partial}{\partial v}\left(v\frac{\partial f}{\partial v}\right)=\frac{\partial^2 f}{\partial u^2} + \frac{\partial^2 f}{\partial v^2}$$

Is something like this on topic/research level?

I've been trying to find out if anyone has solved this before so that I could understand their solution but haven't found anything yet.

  • 3
    $\begingroup$ A PDE is not a question, and only questions can be on topic. What do you want to ask about this PDE? $\endgroup$ Nov 29, 2021 at 13:08
  • 2
    $\begingroup$ I would say: ask it first in math.se if you are not familiar with the PDE literature. Of course, when you ask there you will need to include more than just a random problem statement. $\endgroup$ Nov 29, 2021 at 13:09
  • $\begingroup$ @DenisNardin I wanted to ask about this PDE's solutions $\endgroup$
    – geocalc33
    Nov 29, 2021 at 14:33
  • $\begingroup$ @GeraldEdgar Okay I did that $\endgroup$
    – geocalc33
    Nov 29, 2021 at 14:34
  • 3
    $\begingroup$ @geocalc33 Good luck with math.SE, but in any case, what do you want to know about the solutions? I am very far from an expert in PDE, but my understanding is that an analytic expression for the solutions is pretty much never an option. Often people ask questions about existence, regularity, dimension of the space of solutions etc. $\endgroup$ Nov 29, 2021 at 14:44


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