I am writing a memoir about my abusive childhood. Do I need permission from everyone I write about? My abuser is deceased, but my brothers are part of the story and I don't know where one of them is to request permission, but I don't want to go ahead without knowing I don't need their permission.
You're allowed to publish basically anything you want; the concern is not whether you will be able to publish it to begin with, but whether you can be sued (for libel or misrepresentation) later on. Even if you would win such a lawsuit, it would probably be expensive and a lot of work.
There are two ways to reliably protect yourself from lawsuits. The first is to get explicit permission from the individuals involved; what you want here is a release form, a legal document that basically says "I won't sue you over this book in the future." The second option is to anonymize your the individuals involved - if an individual's name isn't used (or, I assume, directly clear from context), then they have no basis for a lawsuit. That is, if you were to write under a pseudonym and change everybody's names, it would be difficult to connect your actual brother to the character in the book; therefore there would be no basis for a lawsuit. (I do not know what extent of "anonymizing" is necessary - whether name changes are enough, or major identifying details need to be changed as well.)
A few questions you might want to consider:
At any rate, if you do proceed, you should try to get release forms from anybody relevant who can give you one - that's the strongest protection there is. Having one chink in the wall doesn't mean you can leave the main gates wide open.
I relied on detail I found at the following sources: