According to Stack Exchange's trademark guidance:
The website domain name is always written stackoverflow.com (no CamelCase, single word capitalization rules apply).
However in the semi-recent Server Fault blog post, Welcome Shane Madden, ServerFault Valued Associate #0000007!, there's a picture, which implies it hasn't been followed by... Stack Exchange!
I don't think that "Expert" needs to be capitalised either1
1. I know, giant S, please don't kill me.