Buck topology for a 3.3V to 1.1V for a SoC
You could use a linear regulator which would be somewhat simpler (no inductor) but much less efficient. Most of them won't go down to 1.1V because their reference is higher than that. 

It looks like the current drawn by the core can exceed 130mA, so the regulator would be dissipating hundreds of mW from a 3.3V source. 

The suggested switchmode regulator is very efficient and not very expensive. It uses synchronous switching so you don't even need an external Schottky. 

You cannot use a voltage divider in any practical sense, the load current varies too much.