I can see the following sign around,
The elevator is under repair.
Then, how about this?
The elevator is under repairing.
I'd like to know subtle difference between them, if both are available.
"repair" can be either a noun or a verb, and "repairing" can be either a participle or a gerund (a verbal noun).
"Under" is a preposition, and prepositions must be followed by a noun, so both "repair" as a noun and "repairing" as a gerund (verbal noun) are syntactically correct.
There is plenty of information about when to use a gerund rather than an infinitive, but I can't find anything about gerund versus noun, so you will have to take my word for it that in this context, with "under", the only acceptable version is
The elevator is under repair.
I can't think of a situation where "under" + gerund doesn't sound wrong: you always use the simple noun, for example "under construction", "under sentence" and "under scrutiny".
The elevator is
under repairing.
Don't say that. The phrase under repair is a fixed phrase, and the word repair doesn't get conjugated in that context.
An alternative wording would be:
The elevator is being repaired.
And, after the repair is complete:
The elevator has been repaired.
I suppose it would be grammatical to say:
The repair of the elevator is underway.
but that is not idiomatic, and it's much wordier than it needs to be. It sounds "grammatical but irregular."
