According to the DuPont site, http://www2.dupont.com/Surfaces/en_US/produc..., "Soapy water, ammonia based cleaners (not window cleaners as they can leave a waxy build up that may dull the surface) or commercially available solid surface cleaners will remove most dirt and residue from all types of finishes. Stubborn residue will require a little stronger cleaner." The site has a chart for each stain types, other good cleaning tips and is easy reading.
Soapy water, ammonia 50/50, or vinegar will all clean corian counter tops.