Yep, sure are. I'd recommend Plex for this. I believe the iOS app is $5, but the server client to install on the Mini is free. Another popular streaming app I see advertised around here is AirVideo.
One limiting factor to streaming is going to be your ISP upload speed. Try running speedtest.net to look at your upload speed. Anything less than 1Mbps will lead to bad quality. Higher is pretty good.
Edit: Forgot that you were considering Plex already haha. You'll need to forward port 32400 on your router to the Mini to be able to access it from outside of your network.