Building a Corner Support for New Countertops

It sounds like you are just looking for a way to support a counter top. Just install a length of 2x4 on either wall in the corner. The cabinets will support the front edge.

Rygobus

Go see a kitchen designer at a cabinet store or a home builders store, they have a wealth of information that the rest of us do not. If you are buying from a home builder store, then ask the help there, they've built many more cabinets than any of us have. Really, they are great and very patient. Good luck!

You could also do corner shelving with no doors

You could try a lazy susan in the corner. I have two. One in each corner. One of them is next to my stove. The door is small and opens away from the stove.