This question is a lot like asking "What algorithms can I write in Java?" Ummm... all of them? Do a bit more reading about design patterns - they are basically just good solutions to common problems, with advantages/disavantages and other stuff documented about them. There's nothing specific to any app server that will require or prevent you from using any design patterns.
Write once, run anywhere, because there's nowhere to hide! - /. A.C.