Go to this link,and then click on "Caring For Your DuPont Corian® Countertop"
http://www.dupont.com/products-and-s...op-repair.html
There are special micro-surface abrasive pads available, which the table at the bottom of the pdf page shows who makes them. I have found, if you get the top too glossy, you have no chance of using the counter top without adding more scratches to it. A clean, slightly dull finish works for us.