Owner of postgresql database

PostgreSQL privileges are very logical once you get the basic idea.

Each objects carries its own access control list (ACL) that governs who has what privileges on it.

Each object has an owner, which is the user that created it. The owner has all privileges by default, and all other roles have no privileges (there are many exception to this latter rule, for example databases or functions). Only the owner can ALTER or DROP an object.

If an object can contain other objects (like a database can contain schemas or subscriptions, or a schema can contain tables), you need the CREATE privilege on that object to create objects in it.

So let's put that together:

• If you start with an empty database, all the user needs is the CREATE privilege on the database (which would be included in ownership). Then he can create schemas in that database. Since he is then the owner of these schemas, he has the CREATE privilege and can create objects in it.

• If the database you start with is not empty, then you additionally have to grant that user privileges on the existing objects (or change the ownership of these objects). Being the owner of a database does not imply being the owner of all objects in the database.

To answer your specific question, if app-user owns the database, but has no CREATE privilege on schema public, app-user will be able to create new schemas in the database and create objects in these schemas, but will not be able to create objects in public.