In my crontab, neither this,
* * * * * /usr/bin/notify-send "message"
* * * * * export DISPLAY=:0.0 && /usr/bin/notify-send "message"
gets "message" displayed.
This works through command line, but not through cron.
I can't find much on this export DISPLAY addition, though it works when scheduling txt files to be opened through gedit, for example.