A Doubt, An Answer

Q. If Grindelwald had the elder wand, how did Dumbledore defeat him in the duel?
Answer: Perhaps, he was not the rightful owner because he stole it from Gregorovitch and hence he did not win its allegiance. Thus, he succeeded to the extent he succeeded on his own merit and not because of the elder wand. When he faced an opponent his equal(Dumbledore here), he was defeated.