The Harvard deadline for LLM applications is 1st of December but they "strongly recommend applications to arrive on 15th of November". What does that mean exactly ? Does that mean that applying after the 15th is like a late registration and therefore one being late like that will have a smaller chance of being accepted ?

This issue was discussed last year on this board. Have a look at this thread:
http://www.llm-guide.com/board/22577

thank you !

its December 1. Nov 15 is just a preference.

I agree the November 15th deadline is not a sine qua non requisite.

I have sent, however, my Harvard application today and hope it gets their until next thursday, i.e. November 15th.

I sent my Harvard application on 17th, likely to reach there by 22nd. the deadline is December 1, though preferred date was November 15.