Yesterday:
echo date("Y m d h:i",time() -60*60*24); // 24 hours ago.
echo date("Y m d",time() -60*60*24); // yesterday as in date.
As mark pointed out below I did not think of daylight savings. So...
$date = new DateTime(null, new DateTimeZone('Europe/Stockholm')); // Change to suit
$Heretime = $date->format('H');
$date->setTimezone(new DateTimeZone('UTC'));
$Difftime = $date->format('H') - $Heretime;
echo date("Y m d h:i",time() -60*60*(24-$Difftime)); // 24 hours ago in UTC.
echo date("Y m d",time() -60*60*(24-$Difftime)); // yesterday as in date in UTC.
And from there you can convert it back I guess... Or maybe I'm completely lost?