I am trying to show that the *best case* time complexity of Quicksort is $ \Omega(n \log n)$ .

The following recurrence describes the best-case time complexity of Quicksort:

$ $ T(n) = \min_{0 \le q \le n-1} \left(T(q) + T(n-q-1) \right) + \Theta(n).$ $

But I have difficulty in proving that $ T(n) = \Omega(n \log n)$ using the recurrence above.

So how to solve this recurrence?