Quoting "Verified Security of Redundancy-Free Encryption from Rabin and RSA", Chapter 2 (on page 4):
OAEP was proved IND-CCA-secure by Fujisaki et al.  under the assumption that the underlying trapdoor permutation is partial-domain one-way. This is in general a stronger assumption than just one-wayness, but fortunately both assumptions are equivalent in particular for RSA.
- What is exactly are full-domain (and partial-domain) one way permutations?
- Which is the stronger assumption?
- Which is it more secure or efficient?