Asymptotic lower bound of O(n^2)

Question

Are there problems in P that have a proven asymptotic lower bound of O(n^2) or higher? (n is the number of bits a problem instance can be represented by). This is not a homework question, just curiosity.

Answer 1

Yes, the time hierarchy theorem implies the existence of such problems. They're arguably not natural because they involve diagonalizing over all O(n^2)-time algorithms.