Does anybody recognize the original PDE's question?

Question

There was a popular image going around on the internet a while back:

Of course, $ = 1$ and $ = 2$. As for the non-trivial part, $H^{2}_{\text{loc}}(U)$ is a localized Sobolev space and I suppose the rest of the notation is fairly standard. Presumably, $L^{-1/12}$ is supposed to be $L^\infty$, but $\infty$ was replaced with $- \frac 1{12}$ in reference to the Ramanujan summation result $1 + 2 + 3 + \cdots = -\frac{1}{12}$.

I have two questions:

• Does anybody recognize the source of this question? I suspect that it was lifted verbatim (up to emoji-substitutions) from a textbook.
• Does anybody have an answer to the question?

Thanks for your consideration.

Answer 1

According to the comment, this (with further assumptions on $A$) is a standard elliptic regularity result. We should be able to find a proof in an introductory reference such as Elliptic Partial Differential Equations by Qing Han and FangHua Lin.