It depends on the nature, intensity and origin of said domestic violence. If it's exclusively psychological/emotional/verbal or some sort of blackmailing, I'd suggest you try to get this young person to talk about their issues with a professional who could help them and notify their parents/anyone who might be troubling them at home.
However, if this violence has reached physical proportions that could expose the young person to serious and life threatening situations, you should report the case to authority immediately.
No matter what, always try to show concern and support for the child. Knowing someone cares for their safety and well-being can go a long away to encouraging them to speak up.
I hope my advice was useful. Best of luck :)