There are shops that can repair Corian pretty well. They glue the pieces together, then use Corian "dust" to fill the noticeable crack that will be there. Once set and dried, it's then sanded using several grits of sandpaper until it's smooth and clean. It's a long process and requires some skill but a lot of patience.
If you don't care how it looks, simply use a quality glue like Gorilla Glue. A LITTLE goes a long way and it will swell when applied, so use sparingly. Contact Cement works well also. Once you glue it, I would also glue a piece of aluminum underneath and across the break for added support....Dennis