Simple answer: Turn on raytracing. THis is what I assume here, that you're using shadow mapped lights, right? Well they always, and I mean
always leave gaps in places because they are, as the name suggests, maps place on the object to simulate shadows. Or so is my understanding. And unless you put huge numbers in to the resolution spinner in shadow map parameters, you will always get little gaps and badly cast shadows.
So, as I said, the only real way to fix it is turn on ray tracing. Or, you could try adjusting the res of the shadowmaps and see where that gets you, but don't expect miracles.