In 1940 Sobolev recorded the following problem in the Scottish Book, and offered a bottle of wine for a solution.
In 2015, when the second edition of the Scottish Book with updates and commentary on the problems was being assembled, I had some correspondence with the Editor who told me he couldn't locate any progress or find anyone who could provide commentary on the problem. I assume he was never able to do so, since no commentary is included in the published version of the updated book.
I thought I'd post the problem here, and see if anyone in the MO community is aware of the status or can provide commentary. [Note, because of a numbering issue, there are two problems labelled as 188. The other, unrelated problem, is discussed here.]
