If you look up 'cabinets above island' you'll get some ideas but none of those are what I have. My kitchen counter that divides the kitchen from the DR has three units above it held up by two poles and a mounting bracket. The poles are obviously visible but have a nice finish. The bracket at the top of those poles is connected to the underside of the cabinets and not visible at all.
I think you need to speak to a carpenter, or DIY'er with experience, for more info.