Problem using 5V LDO (AP7381) as power source for Arduino
Depending on the actual package for your regulator, the total power dissipation will be limited to something less than a watt. Trying to dissipate more power than this in the regulator will cause it to overheat. To be on the safe side, you should probably limit the power to about 0.5W.

So with 19V across the regulator you don't want to draw more than about 25mA. Your Arduino is probably drawing much more than that, particularly if you are connecting any loads to the output pins.

Your best option is probably to use a dc-dc converter instead of a linear regulator. If you insist on using a linear regulator, you could select one that can dissipate more power...even an ancient 7805 in a TO220 package would be better.