Important results in the theory of PDEs regarding boundary-value problems are trace and extension theorems. Since the trace operator (not to be confused with the trace from linear algebra) essentially acts by restriction to the boundary of the domain, I was wondering how it got the name "trace": who came up with this name, when and why?

(I asked this earlier on [MathOverflow](https://mathoverflow.net/q/283162) but did not get an answer.)