There's a very strong cleaner for pots & pans (and glass) called
"Sokoff." It looks, smells and acts like paint remover, but it
isn't...I've used it on my colored electric frypan (the outside of it)
to remove that baked-on caramel-colored stuff. Works like a dream. Be
sure to follow the directions! On the Corningware, if it has a
"painted-on" design, I wouldn't use it on the design parts - just on
the plain glass parts.

I get mine at the Vermont Country Store, just because I can't find a
local source for it.

N.