I'm looking for a webapp to be installed in a lighttpd + mysql + php
server that allows users to upload theyr own files and download shared
files.

Possibly I need something that allows different levels of authorizations
over directories, for example a root that is world readable, a folder
readable from registered users and writable only from admins, user
folders etc.

Can anybody suggest me an application (possibly opensource) that can do the job?

P.S. The end user skills are limited to opening a web browser (this is
why I can't do it with and ftp server and virtual users).