Bellafill is a tremendous solution for under eyelid hollows.  It has been shown to last at least 5 years.  It is far more predictable than fat injections and after 3 to 6 months, the Bellafill that was injected is replaced with your own tissue so you do not even know it is there.  Finally, the safety profile for Bellafill (number of reported problems to the company per syringes sold) is the same as any other filler.
Here is a link to before and after photos of many patients who have had their undereye hollows treated with Bellafill.