Apple finally has admitted that the graphic chips in the 2011 MacBook Pro machines are prone to failure, and have created an extended warranty program for owners who are experiencing black screens, garbled screens and unexpected shutdowns.
The program covers all 2011 15 and 17 inch MacBook Pros, and mid-2012 to early-2013 15 inch MacBook Pros. 13 inch MacBook Pros and machines without discrete graphics chips are not affected.
The extended warranty program goes until February 27, 2016 or three years from its original date of sale, whichever provides longer coverage.
You can take the machine to a local Apple Authorized Service Provider or Apple Store or arrange for mail-in service. Because it probably involves a motherboard replacement, it cannot be done by an owner.
You can check your machine here to see if it qualifies:
and the program details are here: