MacBook Pro 15 (early 2011) display panel joint is broken, can I get a replacement? The black plastic casing around the display joint has been broken (has a crack). Is it possible to get a replacement for the same?
Yes - Apple runs a repair service through AppleCare although the DIY parts are few to none on that model. You can also buy parts from Apple Authorized Service Providers and they are more willing to hand out parts (usually for a price). I'd start with Apple and go from there to AASP and then perhaps third party providers.

That piece is nearly all cosmetic and as long as wiring isn't exposed or loose to catch / snag / snap, you might be able to fix it with tape or other adhesive by following the take apart manuals posted at http://www.ifixit.com