How can I determine whether a work is in the public domain? Is there a database of public domain works?

There is no comprehensive or definitive database of works in the public domain. It is important to note that public domain laws also vary from country to country, depending on where you wish to use the work. You must check the public domain rules in the territory you are distributing to, before you publish any release that incorporates “public domain” works. 

Various academic and other non-profit organizations collect and share some information about works in the public domain, or may be indicated by a Creative Commons Public Domain Mark - but there is always some risk in relying on this information. Works that have been dedicated to the public domain may be marked with the Creative Commons CC0 1.0 license.