In this Batman Beyond clip one of the Jokers says:
Let's put a smile on that face.
Is there any official source that Nolan got that quote from Batman Beyond and used it for the Joker in The Dark Knight?
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No. While I'm not able to quote a specific example there are literally dozens of variations on this theme in pop culture some from before Batman, or any comics, started publication. "Turn that frown upside down" and "put on a happy face" are just two examples of songs that the Joker has referenced. It's possible Batman Beyond used that particular variation before Nolan but its unlikely it was the first time Joker said it and Joker isn't usually being "original" since he's almost always doing some kind of subversive, ironic parody for his bits.