The dictionary does not list "in elaboration of," but I'd like to know whether it is natural in the following:
Peter delivered a series of lectures in elaboration of the theory.
I'd appreciate your help.
elaborating is encountered far more often than in elaboration of but the latter collocation is grammatical.
The participle is a viable alternative to the prepositional phrase. For example:
defying ... in defiance of
emulating ... in emulation of
honoring ... in honor of
pursuing ... in pursuit of
The prepositional phrase is in a more formal register. Some might consider it a bit ponderous, others as imparting a certain gravitas. A stylistic call. You'd have to consider the ambient tone.