If the machine is having hardware issues (which is probably the case if you did a clean install of the operating system and the issues are still recurring), and they are not the result of any accidental or intentional damage (as grandparent poster stated), they should be covered under AppleCare.

The only exception to this would be the battery (most laptop batteries are only covered under a one year warranty). It is extremely unlikely that your battery is causing applications to crash, though.